The Chain Rule… How? When? (NancyPi)

Published on September 3, 2018 by

MIT grad shows how to use the chain rule to find the derivative and WHEN to use it. To skip ahead: 1) For how to use the CHAIN RULE or "OUTSIDE-INSIDE rule", skip to time 0:17. 1b) For how to know WHEN YOU NEED the chain rule, skip to 4:35. 2) For another example with the POWER RULE in the chain rule, skip to 7:05. 3) For a TRIG derivative chain rule example, skip to 9:33. 3b) For the formal chain rule FORMULA, skip to 11:36. PS) For a DOUBLE CHAIN RULE (or "repeated use of the chain rule") example, skip to 13:33. Nancy formerly of MathBFF explains the steps.

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1) The CHAIN RULE is one of the derivative rules. You need it to take the derivative when you have a function inside a function, or a "composite function". For ex, in the equation y = (3x + 1)^7, since the function 3x+1 is inside a larger, outer function, the power of 7, you'll need the chain rule to find the correct derivative. How do you use the chain rule? You can think of it as the "OUTSIDE-INSIDE" rule: take the DERIVATIVE of JUST the OUTSIDE function first, LEAVING THE INSIDE FUNCTION alone (unchanged), then MULTIPLY BY the DERIVATIVE of JUST the INSIDE function. Sometimes you might hear this expressed as: take the derivative of the outer function, "evaluated at the inner function", times the derivative of just the inner function. For our ex, first take the derivative of the outer function (the power of 7) to get 7*(3x + 1)^6 since the derivative "power rule" tells you to bring down the power to the front (as a constant or coefficient just multiplied in the front) and then decrease the power by 1, which leaves a power of 6. Notice that you leave the inside function the way it is and just rewrite it for now. Then you multiply by the derivative of just the inner function, 3x + 1. Since the derivative of 3x + 1 is just 3, the full derivative (dy/dx) is: 7*[(3x + 1)^6]*3, which is just 21(3x + 1)^6.

1b) HOW do you know WHEN TO USE the chain rule? If the original equation had just been x^7, there would be no need for the chain rule. It's when you have something more than just x inside that you should use the chain rule, such as (3x + 1)^7 or even (x^2 + 1)^7. Sometimes the chain rule may make no difference. For instance, if you have the function (x + 1)^7, taking the derivative of the inside function just gives you 1, so multiplying by that inside derivative of 1 will not change the overall answer. However, it can't hurt to use the chain rule anyway, so it's a good idea to get in the habit of using it so that you don't forget it when it really does make a difference.

2) Another chain POWER RULE example: To find the derivative of h(x) = (x^2 + 5x - 6)^9, use the same steps as above to first take the outside derivative and then multiply by the inside derivative. In this case, the derivative, dh/dx (or h'(x)) is equal to 9(x^2 + 5x - 6)^8 * (2x + 5). Using the chain rule with the power rule is sometimes called the "power chain rule".

3) TRIG EXAMPLE: the idea is the same as above even if you're using the chain rule to differentiate something like a trigonometric function. If you have anything more than just x inside the trig function, you'll need the chain rule to find the derivative. For the equation y = sin(x^2 - 3x), you first take the derivative of the outer function, just the sine function. Since the derivative of sine is cosine, the outside derivative (with the inside left unchanged) is cos(x^2 - 3x). Then, find the derivative of just the inside (of just the x^2 - 3x part), and multiply by that. Since the derivative of x^2 - 3x is 2x - 3, the full derivative answer is dy/dx = cos(x^2 - 3x)*(2x - 3).

3b) FORMULA: Although it's easier to think about the chain rule as the "outside-inside rule", if for any reason you have to use the formal chain rule formula, check out the two versions I show here. Both are based on the equation being a composition of functions, f(g(x)). The second version shown uses Liebniz notation. Either way, both show a component of the derivative that comes from the inside function, and it's important not to forget to multiply by this inside derivative factor if you want to get the right full derivative answer.

P.S.) DOUBLE CHAIN RULE: Sometimes you might have to use the chain rule more than once, known as "repeated use of the chain rule". In y = (1 + cos2x)^2, not only would you need to take the derivative of the outside power of 2, as well as multiply by the derivative of the inside function, 1 + cos2x, but after that you would ALSO then need to multiply by the derivative of the 2x inside cosine because that inside function was 1 + cos2x and not just 1 + cosx. This means you would use the chain rule twice. The idea is that you have to keep taking the derivative of the inner functions until you have reached every inner function that is more complicated than just "x".

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  • haji alhaeri 4 years ago

    thanks 🙂

  • Sara 4 years ago

    Thank you

  • Kush Patel 4 years ago

    Notifications on. Pen at the ready. Whenever Nancy uploads, the math starts.

  • Neural 88 4 years ago

    Good morning from Australia. Thank you for waking me up via youtube notification lol

  • blackpearl 4 years ago

    Can you make a vedio of application of derivatives 😕😇😇😇😇

  • Levi 4 years ago

    cope with heartbreak with derivatives


    • Decaf-Math ASMR 4 years ago

      Levi lol

    • CrazyAlaskanCoDShot 4 years ago


    • KM-16 3 years ago


  • Abel Lopez 4 years ago

    Awesome and oh so true.

  • Wran Ther 4 years ago

    Calculus must be a simple labor of love to enjoy on your Happy Labor Day Nancy! 🙂

  • Varun M 4 years ago

    Give chain rule for integration.

  • Bright Ailemen 4 years ago

    I need a private tutor like you

  • amty 4 years ago


  • Lizard-Truth 4 years ago

    I’m surprised how active you are, so many videos in such short time, it’s a pleasant surprise 🙂

  • Decaf-Math ASMR 4 years ago

    I literally just made an asmr video on the chain rule not too long ago. Nice job! You’re so adorable. People underestimate how hard it is to think, write, and explain at the same time, not to mention your super amazing “backwards” writing 😄 Im glad to find another female MIT grad on here (were you course 18?). I wonder how many of us are on here 😘 Keep it up Nancy!

    • Vikram Bharadwaj 4 years ago

      Lol she’s not writing backwards, it’s mirrored

    • Decaf-Math ASMR 4 years ago

      lol I know. That’s why I put it in ” “. I was just joking because people ask about her writing all the time 😂

    • Vikram Bharadwaj 4 years ago

      @Decaf-Math ASMR 😀

  • Amanda Brito 4 years ago

    thank you <3

  • PhantomWorkz 4 years ago

    Show me as many chain rules as you want lmao. Thank you for the new topic never knew.

    • PhantomWorkz 4 years ago

      The examples were fun and helped.

  • A-KASH 4 years ago

    Love you

  • roberson644 4 years ago

    Man I miss calculus. It was such a fun challenge. The only part I dont miss is exams….. that stress.

  • S. R. 4 years ago

    Can you make some calc 2 videos please?

  • Bush 4 years ago

    This is my girlfriend. You are making me proud babe!

    • Saeed A 4 years ago

      Bush 😂😂😂😂

  • Benhur Bjay 4 years ago

    Do you think you can do a video on differential equations? Just Ordinary differential equations.

  • MR. AJ 4 years ago

    Great video.

  • Jerry Gundecker 4 years ago

    You are making me very smat.

    • Fanime Productions T.V. 4 years ago

      Apparently not.

    • jewjew abrams 3 years ago

      @Fanime Productions T.V. English is for people that dont understand maths

  • San Samman 4 years ago

    this is stuff i know for like 2 years now, i am just watching to hear her voice it so soothing 🙂

    • CrazyAlaskanCoDShot 4 years ago


    • Explicit Tech 4 years ago

      Same but good refresher. Surprised how much easier it is to follow now than it was then.

  • Manuel Gopan 4 years ago

    sin((x^2)-3x) , “It’s trig dont get too excited.” Wts 😂 so nancy is some sort of a mind reader now huhhhhh

  • Kenneth Matthew Villarias 4 years ago


  • Onur HASKİOĞLU 4 years ago

    Hello from turkey

  • Shazal George 4 years ago

    Love you Nancy. You’re really helpful and a life saver. Thanks thanks thanks

  • JCarlo Morales 4 years ago

    Your awesome thank you

  • Johnny Lum 4 years ago

    Can you do some pre cal pls

  • Mohmand Rex 4 years ago

    Thank You Love from Pakistan 😍

  • nirang mathematics 4 years ago

    hi nancy, which technology are you using for these type of recording?

    • palonero 4 years ago

      Um… a marker and a big glass to write on?

  • Nagendran Amarnath 4 years ago

    Happy teachers day nancy

  • Kent Lee 4 years ago

    Your the best Nancy

  • Kris Hammond 4 years ago

    great video thankyou

  • afroz pervaiz 4 years ago

    Tank you for your teaching

  • Fadz Blumer 4 years ago

    Do vectors next please

  • Ronald Jensen 4 years ago

    Stuck with Leibniz’s notation? No, <3 Leibniz's notation!

    • caliguy1260 4 years ago

      Ronald Jensen I’m down wit da Leb too.

  • Faisal Majid 4 years ago

    I’m getting though business Calc by watching these videos.

  • Genius by Design 4 years ago

    How do U do y=(e^(2x))/(sqr(1+x^2) ?

    • Angad Kadam 4 years ago

      Take u=e^2x
      Use [v. du/dx – u. dv/dx] / v^2

    • सर्वहित sonu dubbal 4 years ago

      How fau u take to few uiew

  • Preetam Rawat 4 years ago

    You are very beautiful…

  • Muhammad Ahsan 4 years ago

    You are the reason, I started loving calculus.

    • VIGAX GAMING 3 years ago

      Sahi hai bhsi

    • Pratham Jain 3 years ago

      @VIGAX GAMING hi bhai

    • Prasanna Dongol 3 years ago

      Calculus is the reason I started loving her

    • I’m here to help 3 years ago

      Hey fucker this that’s my avatar

    • EyeZac 3 years ago


  • Anaid Ceniceros Cruz 4 years ago

    I really needed this! Thank you! 💖

  • Fanime Productions T.V. 4 years ago

    For y=(3x+1)^7 couldn’t you just use pascal’s triangle to get the expanded binomial, and then take the derivative of the result?

    • KIYAVASH AZIM 4 years ago

      smartass 😉

  • juan F 4 years ago

    You uploaded this series on derivatives just in time for me to learn it the weekend before a big calculus test. My heroin

  • Will Sampson 4 years ago

    Dam Nancy! Way to go hella deep in the first 15 seconds! lol

    • Zuhayr Ali 3 years ago

      thats what he said

  • CrazyAlaskanCoDShot 4 years ago

    she sounded so sweet and kind at the end that I had to hit the like and subscribe button XD

  • Daniel Dickey 4 years ago

    is she writing everything backwards to her?! O.O

  • Harrison Jendrusch 4 years ago

    “time is the one thing you can never get back” i think to myself looking at all of my calculus homework

    • wadda fuqq 3 years ago

      Imma bout to nut a asymptote on that foreheAD

    • Egg 3 years ago

      Same. My test on derivatives is tomorrow and I’m not even halfway done with the textbook homework at the moment. I thought a few days would be enough. Man, I was dead-wrong. I hate my garbage time management skills.

    • Andy Villagran 3 years ago

      I was dying when she said that lmao

    • Ólavur 3 years ago

      Really made me feel like shit before even beginning

    • Yonnique Williams 3 years ago

      lmaoo. I feel you bruh

  • Amir Zidan 4 years ago

    I love your videos !

  • Andrew Trentacoste 4 years ago

    Thank you for explaining this in a way I can understand. You are one of 3 channels I watch regularly while I plow (struggle?) through my calculus class.

  • Luke D 4 years ago

    You rock. Thank you so much!

  • Trent Mahaffey 4 years ago

    What’s more trippy than the chain rule? How she writes backwards perfectly. Anyone else wonder how she does that?

  • john Mitchell 4 years ago

    Do I need to apply the chain rule before using the quotient or product rule?

    • 暗い影 3 years ago

      john Mitchell No

  • Callyious 4 years ago

    16:30 was quite convincing to like and sub LOOOL

  • Natalie Black 4 years ago

    Thank you! These videos are really getting me through AP Calc.

  • Tooth Less 4 years ago

    She’s using mirror stuff effect. To those who wonder how she wrote at the air.

    • Blah123 2 years ago

      ​@Navya Shetty she edits the video while she’s writing? i guess that’s how she speeds up sometimes too

    • mimi moka 2 years ago

      @Blah123 apparently I understand your humor :))

    • Raghavar Voltore 2 years ago

      @Turbo the Snail The camera itself takes images backwards. So its natural that the flip side will become the correct when viewed into the camera.

    • Felix Runesu 2 years ago

      So she’s left handed??

    • Tooth Less 2 years ago

      She is using mirror as an Item and mirror as an effect

  • Mark Deleon 4 years ago

    Can you please show us how you film this videos because I’m so confused and it’s driving me crazy 😂like do you write backwards??? On a window????

    • jewjew abrams 3 years ago

      She writes normally but then flips the image in her editing software

    • Sendini Randeniya 2 years ago

      @jewjew abrams Is she writing on a glass ?

  • Misael Perez 4 years ago

    Marry me! 😍💕

  • nur b 4 years ago

    You made it so easy

  • Muhammad Tayyab 4 years ago

    helpful video

  • Ants 4 years ago

    These vids help so much!! Thanks Nancy!!

  • Jemwel Pasigian 4 years ago

    What if (sinx+3)^4

    • Pawan Dave 4 years ago

      Jemwel Pasigian need to use chain rule! But same time can also be skipped because sinx is an identity so you can plug in formula.

  • caliguy1260 4 years ago

    I just need you to teach us how to do the fast forward technique
    *because time is something you can never get back*
    Love your videos.

  • Makalin Langford 4 years ago

    thank you!

  • Abdullah 4 years ago

    نانسي مرتبطه ؟

  • Cj Timosa 4 years ago

    Well done… the topic won’t make me amaze but the way of you’re teaching ma’am. BTW Happy Teacher’s Day continue to help other people like me… God Bless…

  • AkaDisilent 4 years ago

    Thanks Pi!

  • M N 4 years ago

    Hi Nancy. I love your videos and thank you for your help. Would it be possible to please show us how to work, let’s say cos(sqrt of sin(pix))? If I subtract 1 from the original power (1/2) I end up with -1/2 which brings the function to the denominator, but will cos go down too, or just what is raised to the negative power?

  • Bea Bramble 4 years ago

    I did maths too long ago to remember…. then found this and it all came back. You’re brilliant at explaining things, thank you!

  • JayTee 4 years ago

    thanks! you earned yourself a sub on the first video of yours i watched!

  • Stephanie M 4 years ago

    I love Nancy so much she had me saved and calmed my stress at 4am for a calc test thanks boo

  • nemo one 4 years ago

    Absolutely clear!Perfect!Thank you so much.

  • Miss Kgrg 4 years ago

    Thank you nancy…you make calculus so easy ….i have learned more from you than my professor. Thanx again

  • Ash aymen 4 years ago

    Thank you you helped me a lot

  • Ibn Abad Alamwi 4 years ago

    getting addicted to the sound of speed @11:45 Amazing 😀 thank you, you’re a great teacher Nancy Pi. 🙂

  • Mr Celle 4 years ago

    Thank you

  • Paloma Aguilar 4 years ago

    Is anyone else wondering how this chick writes calc backwards from her view.. #talent

    • umer waheed 4 years ago

      Then what do you suggest @Austin Aldrich ?

    • Austin Aldrich 4 years ago

      @umer waheed after reading more comments, I do agree with others that the entire video is flipped. Someone said she is normally right handed, but is left in these videos which explains the flipping. I thought they were saying the righr hand side of these videos were flipped.

    • umer waheed 4 years ago

      Man u doin Alev?

    • Noc 3 years ago

      Paloma Aguilar ur a fckin idiot

    • Aditya Panda 3 years ago

      she uses a special board called lightboard

  • michaelperkin89 4 years ago

    Oh Nancy, You ae heaven sent

  • Trains and Lanes Demos & Fun 4 years ago

    I may pass calc now thanks!

  • Diana Ingato 4 years ago

    Wow…first time to watch your video and I feel like at least I’ll answer something in my (cat) next Thursday..good job..

  • Shreya Yadav 4 years ago

    Thankyou Nancy!!

  • Nairu Garcia-Acevedo 4 years ago

    I disliked this video

  • Ambient Soda 4 years ago

    wait shouldn’t your derivative produce a number, and why does the -sin2x become +sin2x in your example? Also when are Derivatives actually used?

  • IttI RmA 4 years ago

    Hello my name is Nahil I’m from Saudi Arabia ,sorry my English don’t good but I want to thanks you you are very great teacher I love watching your videos it’s very helpful.

  • Kush singh 4 years ago

    I wish i had a math teacher like you

  • Aj Mac 4 years ago

    I have a quiz next week and you legit just saved my life thank you

  • nalditwisterron 4 years ago

    what if you use the chain rule, and just end up in a chain of chain rule without getting to the final answer?

  • YoIts LemonBoy! 4 years ago

    these comments make me want to kill myself. people are so cringey.

  • Miguel Barrientos 4 years ago

    Thank you nancypi!!!!

  • Murali Mohan 4 years ago

    Thanks Nancy! Helped me so much!

  • Inan Ismailov 4 years ago

    She’s back 😀

  • Jobobules 4 years ago

    never skipping calculus again if u were my teache

    • Kizy Ismy256 3 years ago

      hihihihihihihihihihihihihihi she just made my life hard u know wat i mean

  • Sevgi Bekiroglu 4 years ago

    Can you do a video on High Order derivatives?

  • Dave C. 4 years ago

    After watching your “Quotient Rule made Easier”, I suppose you could say the Chain Rule made Easier is “dee OUT IN dee iN”

  • Dj Jeon 4 years ago

    I wish youre my math teacher 🙁

  • David Quintero 4 years ago

    I’m a liitle confused. I have the following: e^(9*√x) so “e” is the base and (9*√x) is the exponent. Which one is the outer and which is the inner function?

    • Josh Lucas 3 years ago

      You wouldn’t need the chain rule for that function

  • Joshua Parnell 4 years ago

    LOL that opening was so dark. “time is the one thing you can’t get back.” but it got my attention.

    • Veritas et Aequitas 3 years ago

      And worse, time warns you with a whisper.

  • Al Khaleej 4 years ago


  • Diego Garcia 4 years ago

    I love you

  • Rahul B 4 years ago

    why u so sweaty

  • Chemist Me 4 years ago

    math never been this aesthetic

    • Veritas et Aequitas 3 years ago

      Math has always been this aesthetic. 😉

  • Clutch 4 years ago


  • Branden 4 years ago

    It’s hard to learn calc when you are just staring at her.

    • andres bravo 3 years ago

      Tim Rubin Halcomb damn that’s so powerful

    • wadda fuqq 3 years ago

      stare at these fkn balls lmao

    • Ali Salih 3 years ago

      You got me 😂

    • ArduinoBen 3 years ago

      @Conshisthot bruh

    • Tyrone Jay 3 years ago

      The intelligence is just attractive to most of us.

  • Davey Grimes 4 years ago

    You’re amazing 😭

  • Chris Railey 4 years ago

    This honestly is the best video for explaining chain rule in my opinion. After watching this, chain rule make sense. Never leave YouTube and continue making more!

  • Alex Estrada 4 years ago

    thank you

  • Sem Kjaer 4 years ago

    Im confused, are you writing backwards on a transparent whiteboard?

  • DJ Ango 4 years ago

    You need a video like this but on crack. My professors love throwing shit at us that requires double chain rule + quotient rule + inverse trig derivatives.

    • Veritas et Aequitas 3 years ago

      How do you know which to do first? Do you have an example with solution and work shown?

  • Taimoor Ali Khanzada 4 years ago

    Useful Video,please make a video on How to find general term of a sequence?

  • Del Pino 4 years ago

    These comments lmao

  • Asia Atienza 4 years ago

    lmao I watched Nancy p in high school, look at me now, still watching in uni

    • wadda fuqq 3 years ago

      nancy pelosi*

  • Dorian Karakus 4 years ago

    are u single?

  • Jorge Guizar 4 years ago

    Found this easy when it was introduced in class and this video was good for reviewing for my test.

  • d c 4 years ago

    how did it become -4 and positive sin2x in y’

  • Ray A 4 years ago

    She’s smart, good looking, a lefty and writes backwards. Thanks nancy

  • Indranil Talukdar 4 years ago

    Very good video Nancy.

  • Bernard Sandiford 4 years ago

    Very impressive, getting your material across could be very challenging and I must Nancy Pi does a great job of that.

  • Henos Hussien 4 years ago

    I just want to say Thank Youuuuu Very much. My teacher has made the same question 5 times harder and you showed me a quick way to do it. I appreciate it very much.

  • wss 4 years ago

    your videos help me a lot! <3

  • Jaime Garcia 4 years ago

    Thank you, NancyPi.

  • Emily Reynolds 4 years ago

    “Begging you to use the chain rule” 😂😂😂

  • Emily Reynolds 4 years ago

    “The chain rule is your friend”

  • KAK BRO 4 years ago

    you make it so hard . its very simple . Actually need only few word to explain.

  • Moaz El-sawaf 4 years ago

    Thank you so much ❤

  • shahnawaz* khan 4 years ago


  • Dr.derp 4 years ago

    Please more Calculus videos, great help thank u so much

  • MR MOHANACHANDRAN 4 years ago


  • Kateryna Feshchenko 4 years ago

    Beautiful 😍

  • Jeff Holcomb 4 years ago

    You are doing god’s work

  • Ma Nish 4 years ago

    ThankQ medom

  • KsI DejI 4 years ago

    Thank you for the video, much appreciated keep it up !

  • mathematicaATD 4 years ago


  • Satha nanthan.C 4 years ago

    give me solution for e^-mx sister nancy

  • একাকিত্বের গান 4 years ago

    you are doing the great job

  • dia cue 4 years ago

    lol her stomach rumbling at 5:37 and her just being like um ok

    • Asha Biswas 4 years ago


    • Muhammad Qasim Dilawari 4 years ago

      I’m no saint but pointing that out is just weird ,and the fact that you apparently love it is even creepier.

    • adarsh ajit 3 years ago

      @xogmaster v

    • s on 3 years ago

      That was so hot. I love when unicorns show their human side.

    • s on 3 years ago

      @Muhammad Qasim Dilawari well obviously I never seen a saint named Muhammad before

  • مريض _sick 4 years ago

    You’re beauty more than the math 😂😂

  • Moniker 4 years ago

    The power rule only applies to individual terms of x, not to polynomials that involve x. For (ax+b)^n where x is to the first power and a=1, it is a fallacy to say that it can be solved without the chain rule. Sure it’s easy to look at (x+1) and see that the derivative is 1, and yes if you erroneously apply only the power rule, you will by happenstance come up with the correct answer.

  • Miles Emanuel Paavola 4 years ago

    Thank you for sharing, helps with my engineering studies. 🙂

  • luka p 4 years ago

    Wow great video, helped me a lot.

  • Sk Roza 4 years ago

    I will keep it short n simple..#”WOoooOW”

    • Atukwatse Ronald 3 years ago

      Why then

  • Fernando Jauregui 4 years ago

    what about partial derivatives? works the same?

  • JAX 4 years ago

    YEAH!!! 🤓🤓I’m now a genius. Thanks Nancy

  • 100 Million Subscribers Challenge 4 years ago

    bruhhhh i can’t focus. *i kept staring at her pretty face*

    • abhi nay 4 years ago


    • syed bilal 4 years ago

      Hey..dude…cmon…if u guys keep saying that…then maybe she has to stop uploading videos…

    • Asha Biswas 4 years ago


    • 2c Kf 4 years ago

      @syed bilal exactly you have to stop guys, PLEASE!

    • Agatha 4 years ago

      sub to pewdiepie

  • skeetyeet 4 years ago

    can you do a vid on derivatives using all these rules but for ln

    ex: ln(3x+5)^7= y find the derivative etc etc

  • Yummy Yummy 4 years ago

    You’re amazing!Helped me so much!

  • yuan 4 years ago

    I’m now addicted to calculus after watching this video….

  • Harsh Yeet 4 years ago

    Damn girl! You’re…….. you’re…. awesome

  • Ari Getzlaf 4 years ago

    i don’t think i’ve ever left a youtube comment before but for you, i just have to! i have such a difficult time following most math instruction because i NEED the constant reminders of which rules are being applied where, even for simple things like simplification. You explain things so well, so thoroughly, and are genuinely the best math teacher i’ve ever had! i just wish you had more videos!! thank you a million times over <3

    • wadda fuqq 3 years ago

      You were this years olds when you found out u were gay

  • ashish sahota 4 years ago

    You explain better than all of the teacher in my school’s math department

  • irgski 4 years ago

    I’m hooked!

  • LewStep 4 years ago

    You don’t have to like math.. but you can like my video!.. smooth!

  • KESAVINITHA V 4 years ago

    Thanks Nancy pi Sis

  • #FUN TALKS 4 years ago

    Thanx dear

  • Chris Topher 4 years ago

    you are wayyyy to fucking hot for me to focus properly on this shit

  • rama krishna Raju 4 years ago

    Hi Nancy, i have most of your videos and i really appreciate the efforts you are putting in. Nancy along with these tutorials if you can videos on how to multiply 3 digit, 4 digit, … numbers. Divisions, square and cube roots short cuts etc will be a great help for others and your followers.

  • kamel hatem 4 years ago

    Thanks a lot teacher!!!! honestly for this one i didn’t get even an iota!!!!

  • Brain Gainz 4 years ago

    Are you a 90 degree angle? Cuz you are lookin’ right!

  • abhi nay 4 years ago

    You are soo beautiful as your explanation😍😍😘😘😘

  • abhi nay 4 years ago

    I love u and for upur video also☺☺

  • abhi nay 4 years ago

    Iam from india we get 41 marks in exam .. Tnanxx hod Ill can score full marks for your beautiful video and beautiful face

  • Asha Biswas 4 years ago

    do this…. log sin ( √(x^2 +1))

  • Galat64 4 years ago

    Cant focus on the math.
    Nancy’s gorgeous

  • ramu ganesan 4 years ago

    nice explanation … ma’am , please upload a lesson on exponential

  • apenasmeucanal 4 years ago

    G R E A S E

  • Dawn Ripper 4 years ago

    Idk why people find the chain rule so hard to remember. It’s just d out*d in. For d out, just assume the inner function is x.

  • Tim Rubin Halcomb 4 years ago

    When I took Calculus, the odds were against me. I was a struggling drop out who barely passed the G.E.D. test. However, after befriending a guy and his girl friend who were both engineers, everything changed for me. I had no idea that I had those kind of skills. As a joke, I placed a bet with John and his girl friend. It was a 50 dollar bet. Miraculously, not only did I win the bet, I became quite good in all mathematics. Without any prerequisites, I tested out of college algebra and trigonometry. I then took Calculus 163 and it just seemed so easy. I was also working full time. I liked it so much that I took all of the advanced mathematics courses, and that was at a well known university. I didn’t mean to, but I did make some enemies because I did better than the cream of the crop. In the later courses, the professors graded on a curve, and I controlled it. There was only one other person who came close to doing as well as me, and she was a Jewish Girl so that makes sense. ha ha.
    I’m sorry for the story. It kind of sounds narcissistic for me to be telling a story on your channel. I’m not a narcissist. Rather, just amazed by how I was able to do what I did. All through out my childhood, I thought I was stupid. I was a very quiet kid, but I really got attacked. I mean people literally wanted to kill me, and I will never understand the reason why!

  • Tim Rubin Halcomb 4 years ago

    Oh! Let F(u) = u^9, and u = x^2+5x-6. df/dx = df/du* du/dx.. df/du = 9*u^8. du/dx = 2x + 5. Therefore, df(x)/dx = 9u^8 (2x+5)= [9(x^2 +5x-6)^8] * (2x +5). I used the symbol * to represent multiplication. Great job beautiful. ha ha

  • erick osorio 4 years ago

    My nigga i love yo ass !! Your math help gonna get me out the hood and be an engineer 😂✊

  • LemmeRocK 4 years ago

    14:15 isn’t derivative of cos2x equal to -2sin2x?

    • Muhammad Drammeh 4 years ago

      LemmeRocK I was thinking the same thing

    • Robert Manly 3 years ago

      Yes and that is what she says: (-sin2x).(2)

    • Aarohan Sharma 2 years ago

      That’s what she said

  • - Yaoshmite - 4 years ago

    Do you reflect the video along the x-axis in order for us to read the text? Or do you just know how to write the text in a reflected manner?

  • Bishal Chakrabarty 4 years ago

    Thanks …it is very helpful for me ……

  • ee car 4 years ago

    how did you write on that lady???

    • TrueVerdicts 4 years ago

      She wrote that like she would normally and inverted the video.


    Nancy加油加油 and ignore the comments from polish people

  • Soul of Zion 4 years ago

    tkanhs alot ms. NancyP!

  • Kimkim Be 4 years ago

    why is that the derivative of (-sin2x) is 2? at 14:53

  • Kimkim Be 4 years ago

    how about (9+2t-t³)^6.. does that need double chain rule?

  • mat shred 4 years ago


  • prashant koirala 4 years ago

    you are so hot😘😙😍

  • Usman Shahid 4 years ago

    I know i was listening her the whole time but at the end the way she said to like and subscribe. I Couldn’t stop myself

  • Zulfikri Adnan 4 years ago

    Her voice sounds like the girl from lego who says ‘bye, alligator’ lmao

  • Zenith 4 years ago

    nancy you are amazing love, nice one

  • BanaShawol_ArmyMoomoo 4 years ago

    youtube. a better lecturer than your real life lecturer

  • H S 4 years ago

    when you differentiated -sin2x is the last example isn’t that -2cos2x not just -2sin2x

  • CaptainSchlockler 4 years ago

    Super polished video series

  • Ritik kumar 4 years ago

    that so cute, you are the cutest teacher I have ever seen, your teaching tech. with the smile is osm

    • Tarun Srivastava 2 years ago

      Ritik kumar 🤦🏻🤦🏻🤦🏻🤦🏻

  • Ritik kumar 4 years ago

    every student like me want a teacher like you

  • بهاء فالح عبدالكاظم 4 years ago

    Thank you

  • Albert Serrano 4 years ago

    I wonder why my Australian professor (I think he was a genius) made calculus so hard. I still don’t understand the dy/dx=dx/du, etc.

  • pamodha wickramarathna 4 years ago

    why do the( x^2 + 5x-6)9 answer is not needed to simplify?

  • Rene 4 years ago

    5:36 I hear that stomach growling.
    edit: and at 6:28!

  • mihir shetty 4 years ago


  • gedjecel 4 years ago


  • Moos Sick 4 years ago

    Your voice is so sweet, it is like a beautiful instrument to my ears… by the way your video helps me to recall chain rule… Thanks ☺

  • Thorn Wallis 4 years ago

    helping me graduate grade 12 I subbed xD

  • abello4f1 4 years ago

    Thanks, Nancy!

  • Pia Mari Medalla 4 years ago

    You’re the best at explaining! I loveeee your videos and it helped me a lot! I think I learned more from you than my teacher. God bless you!

  • Carla Luna 4 years ago

    Thank you so much for your videos. You just saved me! ❤️

  • Ally Scholten 4 years ago

    Thank you so much!!!

  • Dina Lark 4 years ago

    Thank you for your videos!!!

  • CLUMSY 4 years ago

    Why did i take Stem at the first place i regret it ..

  • Praise George 4 years ago

    thanks THIS VIDEO REALLY help ME

  • rock22 4 years ago

    you are very beautiful 😃

  • RECTmetal 4 years ago

    I don’t understand why I pay university profs so much when in the end I end up learning all this stuff from talented people on youtube, such as yourself. Thank you for your help!!

    • Riyaad Machaba 2 years ago

      This GIRL IS AWESOME🔥🔥🔥🔥🔥🔥

    • William Kallemeyn 2 years ago

      That’s why I have developed a mindset where I just assume I’m gonna have to learn on my own, from textbooks, youtube and google. If the professor is good, then that’s a bonus, but I don’t expect much from them to start out with. A lot of things are like this in life, Just assume you have to do things yourself, don’t rely on others. Help can be nice, and you should seek in whenever possible, but it’s best to be self reliant first and foremost.

    • NIKHIL SHARMA 2 years ago

      @William Kallemeyn same here … I do the same …

    • BoyBoy Jason 2 years ago

      You have too. People will judge the value of your STEM skills based on qualification.

    • NIKHIL SHARMA 2 years ago

      @BoyBoy Jason yeah , and that’s a bitter truth .

  • Aleer Leek 4 years ago


  • Derin A. Maleek 4 years ago

    why you are so pretty

  • Nathan Underwood 4 years ago

    If my professor was hot id learn so much more ngl

  • Ruthless 4 years ago

    I think I love you

  • Otaku ForEver 4 years ago

    I am here just giving likes… if you got like that’s me 🙂

  • Reggie87 4 years ago

    The real video begins at 9:35. Wish she gave more examples then on instead of from the beginning.

  • James Mclaughlin 4 years ago

    How is the answer any better than the question?

  • Yiqiao Zhang 4 years ago

    Hope you can be my prof 😭 you are amazing

  • Sean W 4 years ago

    thanks for the amazing video, helped alot with the way you explained

  • Sean W 4 years ago

    is the “speed up” noise when she writes satisfying to anyone else?

    • Veritas et Aequitas 3 years ago

      Better than listening… Than listening… Listening… To Sal from Khan Academy… Sal.. saaaaaall… From Khan… Academy… A… Caaad… Emmmm…yyyyy…. Repeat himself… Repeat.. repeat himself…. Repeat himself… Like… Liiiiike… This… Like this!

  • Emily Murdoch 4 years ago

    Such a helpful video thank you!!

  • Dimka /// 4 years ago

    какой приятный голос)))

  • Thoai Phan 4 years ago

    Can you please do a video of combining the Chain Rule with the Product Rule? Thank You

  • Elle R 4 years ago

    ty for the help

  • Agatha 4 years ago

    My teacher is giving us a quiz on this even though we didn’t learn it… Nancy, you just saved my calc mark. You’re a legend !!

  • schmuck Norris 4 years ago

    I know this is YouTube, but I’d rather tell you in person that you are crazy beautiful!

  • shrushti yadav 4 years ago

    Thanks for the help fella…. Really made things easier!!

  • Umily Gopal 4 years ago

    Thank you very much Miss NancyPi I really did learn a lot of very easy methods of understanding the Chain Rule.

  • Francis Gregory Ku 4 years ago


  • Ivegotwo 4 years ago

    these videos would benefit a lot if they were not done in one shot. voice over while writing would benefit a ton

  • James A. 4 years ago

    Thank you cant believe I forgot how to do chain rule… guess I need more practice

  • Joseph Kamau 4 years ago

    you are explaining it excelently. keep up…

  • Roshan Adithya 4 years ago


  • Robin Svensson 4 years ago

    But.. even if you get the 7(3x + 1)^6 * (3) = 21(3x + 1)^6 … you still need to actually calculate that enthire thing? would take decades. Unless you repeat the chain rule until you have nothing to the power of the function. SomeNumber(3x + 1)^1. Not sure if that’s valid tho?

    • Warc Arden 4 years ago

      Chris E No, you only have to apply chain rule once as the question is to differentiate the expression, not reduce it completely by multiple differentiation. You do not need to expand it either with binomial theorem. Its tedious work and is NOT required. Just leave it like that and also do not differentiate the answer again in idea that you’re simplifying, you will get an incorrect answer as differentiating again gives the second derivative

  • TALHA ABDULLAH 4 years ago

    I don’t know if I’m watching this because I’m failing math or because she’s so f****ing cute . now that’s a composite function need the chain rule!!!

  • Katherine Lili Chen 4 years ago


  • ssplintergirl 4 years ago

    took me about 20 seconds to realize you were writing backwards to your perspective. Hats off.

  • Ryanne Chapman 4 years ago

    Can you explain why you don’t have to completely simplify the answers? Is there a rhyme or reason for not doing so?

  • sarah bajwa 4 years ago

    you deserve a nobel prize

  • Wispe 4 years ago

    really amazing video, thanks

  • Tanner Barcelos 4 years ago

    Learned in class today, was lost as hell. Watched this video, 15 mins later, I now understand it lol.

  • Al Soltan 4 years ago

    I don’t speak english
    But learn how to solve derivative from this channel

    Ms. Nancy you are Great

  • Patel Yash 4 years ago


  • A Man 4 years ago

    Don’t get me mistaken I like Maths but, sometimes I feel like jamming a gun right down my mouth then firing till it goes *click*

  • Miguel Martinez 4 years ago

    you are an angel sent from heaven

  • Julianna Evans 4 years ago

    Thank you so much! This is the first math tutorial I’ve been able to sit through because you make it interesting.

  • Chloe Patti 4 years ago

    Okay, so my two friends and I were told to take notes on this video as an assignment. We all agreed that you are one of the best math video producers we’ve ever seen. We also agreed that you have a chill vibe, like to the point where we could make flower crowns together and talk about life with you for hours. Seriously, this is a fantastic video! 🙂

  • Mith Von Voodoo 4 years ago

    Amazing video. Very clear. I really like how you present everything. It simple and you deliver it in a really nice calm way. Feels more like a friend showing you.

  • Aksinia Radaeva 4 years ago

    I never even thought this was possible for a free YouTube vid… but this is better than Khan academy 😄

    • Zach A 3 years ago

      Khan academy is full of smart people. Being an MIT math grad is a whole, notha, level

    • Stiventson44 3 years ago

      To me the khan academy explanation was way better than this, because they demonstrate the chan rule

    • Eli Marburger 3 years ago

      @Stiventson44 please explain what the “chan rule” is

    • Terry LaRue 3 years ago

      @Eli Marburger The “chan rule” is another method of finding derivatives invented by the famous Honolulu detective Charlie Chan.

  • Joseph Chikumba 4 years ago

    realy time saving and easy to remember. thank you nancy

  • Shead channel 4 years ago

    your dress is not perfect

  • Thomas Hickey 4 years ago

    this made the chain rule 10x easier for me to understand

  • VindexAvenger 4 years ago

    Nancy, i bow down to you, thank you! My professor is complete garbage. He spent 2 days on this and i still had no idea what he was going on about. I learned this in 15 min thanks to you.

  • M H 4 years ago

    You made my life easy!!!! Thank you so much .. wish you were my math professor

  • noonesflower 4 years ago

    is this woman writing backwards?

  • Platinaezel21 4 years ago

    At the second example, why didn’t she distribute 9 to (2x-5)

    • Warc Arden 4 years ago

      vincent baldonado That would be quite difficult to distribute, Not only would you have to use binomial theorem to expand the octa polynomial but then you would have to distribute it again with a linear polynomial. You never have to do such things.
      you can leave it undistributed

  • Malathi Bhat 4 years ago

    You teach great Nancy! Wish you were my maths teacher

  • Malathi Bhat 4 years ago

    How do you differentiate X(sin(X)^2)?
    Could you pls explain

    BTW you’re the reason why I love calculus. Thank you😁😘😘😘😘😘😘😘😘😘😘😘♥️♥️♥️♥️♥️♥️♥️

  • Robert Vandenberg 4 years ago

    I wish I could have a math teacher like you. My math would have been way better than now.

  • الملك تحتمث الثالث 4 years ago

    you are so cute !! i imagine that i have your number!😅

  • Emmanuel Nava 4 years ago

    I wish my professor was as pretty as you

  • Jasmine Joaquin 4 years ago

    How do you know when to stop finding the derivative? Like you could take the last bracket of the things you’ve solved and solve for the derivative of that.

    • Warc Arden 4 years ago

      Jasmine Joaquin You only differentiate the entire expression once, till you get to the innermost function. Don’t differentiation the derivative again because that would give the second derivative which you probably do not want.

    • Jasmine Joaquin 4 years ago

      Fen boii Got it. Thanks!

  • kalindawalo mwansa 4 years ago

    man i thought i was done w this channel after hs now look at me, back here with this on repeat at awkward hours in uni

  • Srujan Bhirud 4 years ago

    how do she edit the board/ surface on which she writes??

  • Sonia Gesmundo 4 years ago

    Great work!!!! Thank you!!! It really clarified a lot of things!!

  • Nima Mehdizadeh 4 years ago

    that is great

  • Paul Koita 4 years ago

    What if there’s a cube root

    • Warc Arden 4 years ago

      Paul Ps x^1/3

  • Jeevan Sidhu 4 years ago

    How can i concentrate on the video, with this peng ting explaining it to me?????

  • PBS Alyid 4 years ago

    Nancy can’t thank you enough! U at a Doctorate level….

  • jimmicrackhead12 4 years ago

    Wow, how does she write backwards so well?

  • Mariano 4 years ago

    Master The Chain Rule And Get Familiar With All The Notations. Gotcha

  • yuchuan yang 4 years ago

    can you also do videos/ lessons for AP calc or for college students? same thing but more challenging questions?? thank youu

  • my life 4 years ago

    Hey, i’m new to this topic, I understand everything except the end example14:49, where you got rid of the Negative sine

  • Raunak Chaudhary 4 years ago

    Very sexy maths

  • Christine Ren 4 years ago


  • Ryan Ahmed 4 years ago

    why did the -sin turned into just sign? 15:30

    • Taylor 4 years ago

      Raeean Ahmed the negative moved to the front of the function. In front of the 4

  • Anaa Shukla 4 years ago

    Ma’am I’m from India you explain the thing in such a good way with clearing the concept like no other Thank you so much ❤❤

  • Jasman Dhillon 4 years ago

    Thanks I learnt my most difficult topic

  • Malyuun xashi 4 years ago

    thank you nancy💕

  • Thabiso Dlamini 4 years ago

    so i watched the video earlier before, now im back

  • Shinchan 4 years ago

    💗 🇹​🇭​🇦​🇳​🇰​🇸​ 💗

  • Eric Bridge 4 years ago

    At school we’ve been learning this for over 2 weeks and we are having a test tomorrow on it. All this time I understood absolutely nothing at the class but now I watch a 16min video and understand everything xD

  • Viraj Vardhan 4 years ago

    What does she write on???

  • Beatz Drop 4 years ago

    You understand everything when your teacher is not, love you Nancy

  • Vandit Gujrati 4 years ago

    Thank you so much 😍👑

  • Tart Pop 4 years ago

    Thank you this really helped

  • Jubo Mdivnishvili 4 years ago

    Everything is crystal clear. Thank you!!!!

  • Murphy Diep 4 years ago

    Your explanations are great, I understand the concepts and process well. But I’m a blind math student, and sometimes it’s difficult to follow along because you don’t say what the functions are at the beginning. You completely rely on the audience to use their eyes and vision to see the functions for context. As one of your viewers who is blind, I sometimes get lost because I don’t know what the function is or what numbers/variables in which you are referring. You mostly say, “this” instead of saying the actual function or numbers. Saying “this” less often and the functions and actual numbers more often would greatly help me with context and understand the numbers you are referring. Your explanations of the concepts are great and clear, adding verbal and audible context would be a great accomadation for me.

    • Faze Eugene 3 years ago

      Murphy Diep I respect your work ethic man, keep it up.

  • Shrey TM 4 years ago

    Thanks for your help!

  • chronicsnail 4 years ago

    How tf do you write backwards

  • Cheikh Camara 4 years ago

    Hi Nancy, which program do you use to write directly on the screen?

  • Pablo Loves You 4 years ago

    15:02 how did you get -4 and positive sin2x

  • Ali Zafar 4 years ago

    That ending was pretty climactic, I must say.

  • jonathan feliciano 4 years ago

    lmaoo these comments are hilarious. Focus my children.

    • Coders Hub 3 years ago


    • Coders Hub 3 years ago

      You are right.

  • Hammad Pansota 4 years ago

    Thanks. It was helpful ❤️

  • 15,000 Subscribers With No Videos Challenge 4 years ago

    The most impressive thing is that she’s actually writing backwards!!!

    • k k 4 years ago

      I don’t think so lol

    • Nihal Ishac 4 years ago

      sorry no, the video is just flipped

    • Aarohan Sharma 2 years ago

      Ummm no

  • Waleed Muhammad 4 years ago

    i love you

  • adwnaras FTW 4 years ago

    ti les mori

  • Jar汁機 4 years ago

    you are left handed

  • George Preece 4 years ago

    luv u nancy

  • Jayanti Shankar 4 years ago

    Thank u soooo much

  • Jefferson Umara 4 years ago

    like my comment if u think she explains better than most of our lectures

  • Martin Pettersson 4 years ago

    Hey Nancy!

    Whats your sine? It must be pi/2 because you’re the 1

    Thx for the videos, i still have passed calculus but i think i Will soon thx to you 😎

  • mohammad javadipour 4 years ago

    its very difficult to concentrate on the topic,,,once u r in the screen!

  • Alan Duncan 4 years ago

    Calculus taught me the most important lesson I ever learned in school. Don’t take a class at 7am five days a week. On the bright side though, I always got a good parking spot!

  • Ya Yeet 4 years ago

    calc final in an hour… you are a life saver.

  • Chris Davison 4 years ago

    Thanks Nancy, I always watch you when I feel like I should be studying but have been distracted, you have a knack of bringing me back. I owe you the 1st I’m aiming for. Couldn’t have done it without ya. 😉

  • Gabriel Shapiro 4 years ago

    “When do you use the chain rule? When you have a more complicated inner function…”

    NO! Use the chain rule ALWAYS!!! The chain rule ALWAYS applys!

    Say you want to find d/dx of x^2

    You still need to use the chain rule.
    1. Power rule – bring the exponent to the front, then subtract 1 from the exponent – you get 2x
    2. Chain rule – multiply by the derivative of the inside function, which, in this case, is 1, so it doesn’t change anything. But the chain rule still ALWAYS applys.

  • JOY PHOKU 4 years ago

    love you NancyPi

  • Odette Kings 4 years ago

    This helped my soul

  • Zerg Fx 4 years ago

    Nancy, I thank you.
    I have computer aided geometric design exam in 2 days, and I needed to remember this quickly, because school was way too long ago and I kind of forgot what this was about.

  • Whitestar 4 years ago

    hey say you have an exponent like 2^(2x) how would you do that

  • Jag Singh 4 years ago


  • Axole Manoni 4 years ago

    She is good. Thank you so much

  • oya kesgin 4 years ago

    omg you explain so well. thanks

  • Bhavin Rana 4 years ago

    U teaches very nice were do u live mam 👍👍👌😇😇

  • ratzasse 4 years ago

    I think I get it. So, if that’s true, then the derivative of x cubed would be 3x squared?

    • Mitchell N 4 years ago

      ratzasse yes

  • Jerry Whang 4 years ago

    simple stuffs

  • New Life Loading 4 years ago

    Wow you made it much easier than it was expected to be
    You’re amazingly smart

  • Daniel Kelly 4 years ago

    Now that I realise why it’s called chain rule it all makes sense!

  • jelly ace 4 years ago

    ok hold up is she actually writing in reverse

    • Stardust Lordfinery 3 years ago

      No she flips the camera

    • jelly ace 3 years ago

      Stardust Lordfinery thank god cause I was wondering about it the whole time I was watching her videos lmfao

  • Rajeev Sharma 4 years ago

    Mam, it was really helpful. Thanks a lot.

  • Jim Keller 4 years ago

    This may be the clearest video I’ve ever seen for math.

  • Theekshya Nuwanthini Kularathne 3 years ago

    You are so beautiful

  • joel simakando 3 years ago

    whaaaoooooo!!!!!!!!!!!!!!!!!!! this is soooo nice your explanation is really helping.. THUMPS UP

  • Ahmed hope 3 years ago

    I couldn’t focus more on the board then I do on YOU.
    Thanks anyway

  • -- 3 years ago

    What happens if there is no power outside the bracket? Does that mean the power is 0 then you minus 1 so it would be to the power -1?

    • Warc Arden 3 years ago

      if there is no power it means thats its raised to power 1 not 0. anything raised to 0 equals 1

  • Nathan Samson 3 years ago

    Never liked maths cos i it was never xplained the way its done Nancy Rox

  • Ted Wazish 3 years ago

    Great as always

  • dsalaz04 3 years ago

    Is she writing backwards?

  • Shreyansh Arya 3 years ago

    Wonderful explanation………ma’am……..lots of respect from India…..😊😊😊😊

  • im Savage 3 years ago

    khan academy + nancypi got my back

  • Sean Hanley 3 years ago

    Loving, cough cough, math😍😍😉

  • Deepu Sur 3 years ago

    Can we not apply product rule in the se questions.

  • tejas patil 3 years ago

    I really love you.
    I mean your videos.
    p.s -love you too

  • Klyntoh _OvO_ 3 years ago

    Me:I don’t know calculus but i know i love you.Will you marry me?
    Her: 6:09

    • Sarthak Bisht 3 years ago


    • Brajendra Pandey 2 years ago

      An what if it was 9:04?

    • Aarohan Sharma 2 years ago

      Ha u wish

    • Oh Wow 2 years ago

      Also her: 9:41

    • U K 2 years ago


  • Bhagyawati 3 years ago

    Is The Video Flip Or You Know How To Write Mirror Letters

  • Sfiso Thwala 3 years ago

    Thank You!!

  • Secret Passion 3 years ago

    Wow…mathematics is also beautiful when some gorgeous lady is teaching it!

  • parasmani sharma 3 years ago

    I learned today that mathematics is also beautiful.

    • parasmani sharma 3 years ago

      Thanks for such easy explanation.

  • nawaz najju 3 years ago

    Nancy s hot😈😈

  • Priyank Tongar 3 years ago

    How can we solve -sinx^1/2 🤔
    😌 Please reply

    • Life Unfair 3 years ago

      dx/dy=-cos(x^(-1/2))*1/2 =-0.5cos[1/√x]
      Treat initial (-1) as the constant, know that the derivative of sin is cos, and treat the inner function as x to the power of 1/2. Easy, man!

    • Priyank Tongar 3 years ago

      @Life Unfair Thanks bro

    • Life Unfair 3 years ago

      @Priyank Tongar You’re very welcome bro! Enjoy the Maths!

  • Rihana Fernandez 3 years ago

    Those are very useful..thank you nancy..

  • Rahul G 3 years ago

    I would not skip any maths class if the teacher was this pretty.

  • SUMIT KUMAR 3 years ago


  • Saul Alvarado 3 years ago

    Hol’ up, girl. How are you writing backwards like that? 0_o

  • Reinaldo Fanuel 3 years ago

    Don’t have to like math but I have to Like your video

  • PhysicsBro 7129 3 years ago

    I like the way of teaching very easy to understand! Keep it up!

  • Jabir khan 3 years ago

    Looked many lectures but didn’t understand chain rule..
    Thanx mam u have done a great job..
    Love from Pakistan

  • BIPIN CHAUDHARY 3 years ago

    You should to give more examples

  • Erin 3 years ago

    Thank you so much! I’ve been struggling with derivatives for some time now and really appreciate you doing this

  • Jacob C 3 years ago

    I just realized you’re writing this all mirrored! And left handed! Wow!

    • Veritas et Aequitas 3 years ago

      No, she isn’t.

      If write normally and right-handed on glass and film from the other side because it’s easy and shows a good view, it’s backwards. Now just mirror the image, and it appears left handed and forward again.

  • NRRI discipline nepal 3 years ago

    good from nepal

  • Athiambo Nyabundi 3 years ago

    Like. Like. Like.Like

  • Allison Osornio 3 years ago


  • Sohan Nikam 3 years ago

    It’s like you good

  • vincent wekesa 3 years ago

    Awesome teacher!

  • Jim Novack 3 years ago

    This is a good refresher on derivatives.

  • Aditya Chaudhary 3 years ago

    Wow 😍 i never knew calculus was so easy. All bcuz of u mam. Thank u 😅. Was wondering if u could tutor me 😍

  • Alexandre Magno Borges Tanck 3 years ago


  • zein norman 3 years ago

    U EVOL I

  • zein norman 3 years ago

    how you can do that ???

  • Muhammed Safthar ma 3 years ago

    Excellent performance

  • Dan Strayer 3 years ago

    I would like to see a maxima-minima problem

  • George Missailidis 3 years ago

    The chain rule directly follows from the outside-inside rule. They are essentially the same, just said differently for different circumstances.

  • Life Unfair 3 years ago

    Nice job Nancy! Thanks for videos and keep on!

  • javier v. 3 years ago

    I’m an electrical engineer nearly ten years out of school, BSEE/MSEE, it’s midnight and I’m watching Nancy’s videos and I have to work tomorrow 😂

  • abdy Shire 3 years ago


  • Crescent Appu 3 years ago

    very helpfull keep going!!!

  • uzoma favour oluchi 3 years ago

    Just came across your channel. its really educative and easier to understand. Thanks alot

  • Cake Themba 3 years ago

    Nancy…you are really making my life easier….im a fist year student and the way you teach its 100% awesome thank you

  • Albert Batfinder 3 years ago

    They wasted the title “A Beautiful Mind” on some film about John Nash.

    • wolf dog322 3 years ago

      Albert Batfinder no they didn’t

  • Neel Patel 3 years ago

    Do you actually write back to front in the video or
    is it added after? If you do write it the hand writing is better than my normal writing ✍️

    By the way thanks for the videos. I’m about to start a data science bootcamp, these videos are going to so useful as you explain things so well. Thanks!

  • ARPTICS 3 years ago

    Great video and explanation. Thank you Nancy.

  • Missing Name 3 years ago

    This is what iam looking for thank u mam

  • NIRMAL PJ 3 years ago

    That’s informative

  • Mark praire 3 years ago

    she likes to swim

  • Heaven Mood 3 years ago

    thanks, I learned so much from you and got in love 😍

  • Toby Wilson 3 years ago

    I ‘ll take door number 4 drew

  • Bob Channell 3 years ago

    Thank you for posting this series of videos on directives. I’m learning about machine learning, but I don’t know calculus, so these videos are just what I need. I would be happy to watch one more video, that covers the last three examples you showed us in this video. Also, you’re really gorgeous.

  • Mist R 3 years ago

    I should be paying you instead, not my uni teachers. Thank you so much.

    • Vinícius Teixeira 3 years ago

      Nice profile pic

    • Mist R 3 years ago

      @Vinícius Teixeira it dj0nts mate

  • Satyam!! 3 years ago

    Thank u Nancy….I didn’t understand it in school….love from india

  • ROZ Gaming 3 years ago

    This is amazing to study like this you are awesome teacher thanks.from India🇮🇳

  • Suyash Purwar 3 years ago

    Thanks a lot

  • Terje Oseberg 3 years ago

    Damn! She writes so fast!!!

  • Mohamad Ibrahim 3 years ago

    Learned a sem worth of classes in three vids. Thank you for my making life easier.

  • sting aling 3 years ago

    “It’s Trig. Don’t get too excited” !!!

  • joash 3 years ago

    that blouse just like math looks really good on you

  • ksungjin10 3 years ago

    Are you a lefty or righty?

  • Priyanga Smith 3 years ago

    Amazing! Thank you!!!

  • Anuj Gokhale 3 years ago

    Ma’am u are so beautiful😍😍😘😘❤️.
    Also thanks for explaining such difficult topic ..
    Luv u ma’am.

  • Nivesh Bhave 3 years ago

    Your so gorgeous Nancy❤️

  • Hamid S 3 years ago

    I smashed the LIKE button lol

  • B J 3 years ago

    I wish i had a teacher like you in my college.

  • Dean Gaspar 3 years ago

    Hi how would i solve e^kt sin(at) i have been told the formula changes to f’g+f g’. Is this true?

  • Gaurav Salunke 3 years ago

    You know the multivariable calculus

  • Gaurav Salunke 3 years ago

    There is chain

    • Gaurav Salunke 3 years ago

      Also chain rule is

  • Jackson Rupert 3 years ago

    How tf is she writing backwards the whole time? And she’s left handed!

    • Jenny Arachovity 3 years ago

      my question exactly?!?!?! what is this sorcery

  • whiteburr 3 years ago

    I just wanna know what shes writing on. It looks like shes writing backwards on a glass pane and then it erases itself without a scene change! Who is the producer of this masterpiece??

  • RECOO AL_SAADEY 3 years ago

    فديتج تسوين كل دكاترة جامعتنا

  • Luis Fernando Tarazona Herrera 3 years ago

    The last part is a little conffusing will you please explain with otger examples more furthr PLEAAE Nancy ?????

    • NancyPi 3 years ago

      Hi Luis, which part do you mean? The Double Chain Rule part? Or the e^(3x) and ln(5x) part?

  • Stephen Lewis 3 years ago

    Hi Nancy! Do you have a video that explains how to apply the chain rule ro the problems at the end of the video? I’m referring to e^3x and ln5x. The rest of your video made perfect sense, but these are a little hard for me.

  • M Co Tech TV 3 years ago

    How to write like you opposite side please tell me

  • अटल यादव 3 years ago

    I want to marry I was totally impressed

  • A. Brantley 3 years ago

    got through the whole video without learning any math. Distracted by how shes writing backwards

  • Maths Mantra By Abhishek Dwivedi Sir 3 years ago

    Very nice Video

  • Maths Mantra By Abhishek Dwivedi Sir 3 years ago

    I am going to upload a Video of All Questions of old papers of IIT Differentiation. So just check that out. Thank you

  • Matemática Fácil com Prof. Juarez 3 years ago

    Thanks a lot. I am Brazilian but I could understand well. I loved the video.

  • Nnaemeka Azih 3 years ago

    i never thought cuties could be this smart

  • Rosemarie Dagohoy 3 years ago

    Good teacherrr for realll!!!

  • mich mich 3 years ago

    why is the derivative at 14:52 2??? I thought it would be cos2x or somethin :v

  • 작은행복 3 years ago


  • Trash 3 years ago

    Is she writing everything backwards

    • jk masters 3 years ago

      i thought i was the only one who noticed this, but I believe she writes regularly and the video is reflected

  • Miss Rosie 3 years ago

    Nancy thank you very much, u are a blessing!

  • Maxens 3 years ago

    Thank you so much. Our teacher explained this in such a convoluted way that I understood none of it, plus it took her a long time to explain, and I understood none of it without even being able to point out what I didn’t understand (since it was none of it). French math teachers are so verbose…

    • Maxens 3 years ago

      Turns out I managed to forget how to do this in five days only! Thanks brain! THANKS!

    • Maxens 3 years ago

      Slowly starting to think that my brain likes Eastern Middle Aramaic, not math.

    • Aarohan Sharma 2 years ago

      French + Tough ass Calculus = Ugghh

  • Hamza Shabib 3 years ago

    I hate math, but with you it’s us that’s adding up😎

  • Daniel Johns 3 years ago


  • Inquire98 3 years ago

    “Thank You”, thank you very much ☺️, that was REALLY good 😎

  • SHADOW THE GAMMER 3 years ago

    Hit like if you had clicked on the video and directly go to the comment section..😅

  • LorD TwisT 3 years ago

    Wow my lecturer took 1 and a half hours to teach this🤣

  • Hani Saymeh 3 years ago

    Most beautiful Math teacher in the world. <3 who agrees?

  • Nikki W 3 years ago

    5:36 heard a tummy growl

  • LK-4D4 3 years ago

    Thank you for this. So much easier!

  • CM Tabamo 3 years ago

    cant focus on the topic because of such beauty😍

  • Naomi Nagata 3 years ago

    This is very concise! Also I love the part where it speeds up! Thanks, Nancy!

  • momo s!!!! 3 years ago

    Thank you so much for your lesson.Even I don’t speak english fluently, your explanation was very clear.

  • Prajwal Chavan 3 years ago

    Mam u r so good a person to Learn from… But u r looks are quite catchy…u look so damn good

  • Nigel Wright 3 years ago

    One of the best videos I have seen on derivatives, well done.

  • Athira Uday 3 years ago

    thank you
    you did a great job

  • MJ C 3 years ago

    Nancy you’re awesome. You help me more than my calc professors 😪

  • WHEELZZ 3 years ago

    what if you had sin^2(3x) do you have to keep taking the derivative of the inside function until you can’t derive anything else

  • Brandon Blank 3 years ago

    Pretty and smart

  • Jyoti Ranjan Jally 3 years ago

    Awesome 👏🏻

  • ONE Treasure 3 years ago

    Can any one tell what if its (x^4/x^2+1)^8 can i use a chain rule with this, please anyone help me

  • HillbillyfromAL 3 years ago

    Nancy I know your wizardry secret but I won’t spoil the mystery for others 😉 I would love some more derivatives of trig functions I’m struggling with remembering those. Thank you and you have no idea how much you’re videos have helped me over the years.

  • Gabriel Guiote Ribeiro 3 years ago

    Great class!!!

  • Abdirazak .A 3 years ago

    thank you very much

  • scribble71891 3 years ago

    Ah the chain rule, the one rule of derivatives I hate more than anything else.

    • FlameVille B.I.C 3 years ago

      Same. I am literally in the midst of a mental breakdown

  • Sheldon Francis 3 years ago

    15:00 Why neg. (-)4? I never understood that.

    • Akin Pedro 3 years ago

      She took the negative 1 from the (-sin2x) and put it in the front since (-sin2x) is the same as (-1)(sin2x)

  • Akani Yusuf 3 years ago

    Nancy thanks for every thing I’ve suggestion plz make parts like (part 01)

  • Christopher Cabintoy 3 years ago

    thank you

  • Shaburu 3 years ago

    shouldn’t the written stufff be flippped

  • Kristy Wilday 3 years ago

    Hi Nancy, you make it all seem so simple. What if you have cos times pi t sin pi t. I don’t know how to put in the pi sign.

  • Leansifer 3 years ago


    • Лейла Ахмедова 3 years ago

      buddy, have you passed it?

    • Leansifer 3 years ago

      @Лейла Ахмедова hell nah brah I’m probably gonna have to retake this shit, all good though, don’t let your memes be dreams

  • ANUP KUMAR 3 years ago

    Mam aap London se lagti ho

  • An Huynh 3 years ago

    Thank for your wonderful video! You’re such an amazing, beautiful and mathematics youtuber!

  • Qishi Li 3 years ago

    wait a second… how do you write everything mirror-inverted?

  • Way Cool 3 years ago

    Your handwriting backward looks better then my normal handwriting. Sign me up for your handwriting class.

  • Chong Wei Yan 3 years ago


  • Teddy W.C harawa 3 years ago

    You are fantastic. I am in love with Calculus because of you

  • Hastin Nuraini 3 years ago


  • Steward Kaisi 3 years ago

    Really love the video. The expaination was clear enough to understand

  • Ali Hashimi 3 years ago

    Swear, wish you were my teacher. You’re relatable and know how to teach.

  • Gregory Oliver 3 years ago

    growing up all of my math teachers were white males and racist white females. I was considered ‘slow’. but for some reason when i exit the classroom where I was the only black guy that had to get lower grades so that my white peers could look better, all of a sudden math is simple, its fun. But hey even Einstien was thought of as an idiot at math at one point.

    The way your caring and nurturing for your audience, really shows the value of females in teaching roles, without ego and truly looking out for the best interest of your students.

    In a word thank you.

    *and gotta ask…u single?…hahah

  • زياد بخاري 3 years ago

    I can’t concentrate in the lesson she is soo beautiful

  • Bob Tripp 3 years ago

    Thank You Nancy

  • SaravanaKumar Tiruthani 3 years ago

    Great videos, Nancy! I bumped into your video when I was looking to help my kid with math. I found the way you have captured the writing with you behind is truly awesome! Could you share how you got this video? Are you using a glass facing the camera (in which case, you will have to be writing in mirror reflection)? Are you using any cool tech / vendor?

    • SaravanaKumar Tiruthani 3 years ago

      Found another youtube video explaining how this was done. The video was shot with the presenter writing on the glass, and the video was horizontally flipped using Windows Movie maker (or equivalent software).

  • DivasAndKnouckouts44 3 years ago

    Thank you!

  • Yung Rich 3 years ago

    Thank you very much..God bless you.

  • Yung Rich 3 years ago

    I’m done of’ll always be my lecturer

  • Om Puri Gosain 3 years ago

    How do you write?

  • BISMARK KANAH ATSU 3 years ago

    Thanks for the lesson
    My class teacher taught me exactly what you did

  • David Lappert 3 years ago

    Nancy “time is the one thing you can never get back” Pi

  • Spencer 3 years ago

    Ah yes ten grand a semester to lookup youtube videos online after lectures. Quality education America…

    • Aarohan Sharma 2 years ago

      What r u talking about bro? Come to India …. See how we play here

  • Clifford Williams 3 years ago

    Thanks Nancy!

  • Persy López 3 years ago

    Than youuuuuuuuu

  • dadju Yal 3 years ago

    Does anyone know why it’s -4 at 15:02?

  • kanye west is the greatest rapper of all time 3 years ago

    class with her would be so much easier, so hot

  • Audioholics 3 years ago

    Dear Nancy, your presentation is inspiring me to do advanced math again despite I’ve been away from it for nearly 2 decades. Thank you for doing these videos. Simply superb! You should definitely be monetizing this channel more. You deserve it!

  • Optional Dares 3 years ago

    Amazing , thank you for these great videos

  • Noc 3 years ago

    Shes hot

  • Stacy Yardley 3 years ago


  • Angel Dejesus 3 years ago

    Wow thank you so much!

  • Chris Main 3 years ago

    0:22 When she asks herself questions, says “those are excellent questions” and then smiles at her own joke <3

  • Michael Giron 3 years ago

    Wow she Is sexy

  • Chance 3 years ago

    How is she so cute

  • MIKE SONG 3 years ago

    you are so beautiful.

  • Michael Karapetian 3 years ago

    You’re my hero

  • prasant panda 3 years ago

    14:55 how the derivative of -sin2x is 2? Its supposed to be -cos2x….right? Someone please explain🤔

    • G.Robert 3 years ago

      just take the inside function as 2x. derivative of 2x is 2.

  • William Hough 3 years ago

    nancy, you and your mannerisms are like the female equivalent of Harry Miree. quite a good thing, he’s awesome!

  • Jules Verne 3 years ago

    The Derivative Calculus of (3x +1)^7 = 21x +1!!!!…. You just can”t throw away the “3” to get (x + 1)^7…. What happened to the “3” , you cannot just throw the “3” into thin Air?!

  • Harry Youmans 3 years ago

    What a pleasant way to tackle the chain rule. You have a gift, I hope you intend to explore it by sharing it with all of us frustrated calculus students.

  • manju goel 3 years ago

    when there is -sin2x we took x bcoz of derivative of inside function but y did -sin2x stayed like that wont -sin get derivative

    • Jonathan Bryant 3 years ago

      Hey, I thought it would dy/dx of cos 2x was -2 sin 2x am I wrong?

  • Mjd Ilast 3 years ago

    Very good explanation, good job Nancy . Thank you

  • kanan kanan 3 years ago

    Can i Marry you?

  • Movie Walker 3 years ago

    why do u speak to us like we are 5 years old.

    • Pheeshi 3 years ago

      Tinsae Aregawi i don’t see how. Not sure if it’s even possible to explain calculus to a 5 year old; doesn’t matter what kind of vocab you use

  • Zeus R 3 years ago

    For the trig problem Sin(x^2-3x) why wouldn’t it be the product rule if the exponent is 1?

  • mwangi muchiri 3 years ago

    great but didnot full understand double chain rule

  • Moe Alsak 3 years ago

    You are amazing, thank you

  • Seth Rhoten 3 years ago

    is nobody else amazed at the fact she’s writing this backwards every time???

  • Bhavik Upadhyaya 3 years ago

    I hate calc so much

  • DEV PARASHAR 3 years ago

    Tu meri maa k saman hai MAA mari RAM RAM

  • Ashraf Mammadov 3 years ago

    I watched other youtube videoa about calculus, I even tried udemy courses, but non of them have not explained as clear as this lady.

  • Misheck Bonongwe 3 years ago

    thanks for your help

  • Jonathan Bryant 3 years ago

    14:22 Please can someone help me, I was under the impression that dy/dx of cos 2x = -2 sin 2x. However it is written as -sin 2x as if there wasn’t a constant before the x.

    Any help would be much appreciated. Thanks.

    • alex rider 3 years ago

      She put it as (-sin2x)(2) instead of -2sin2x….she was just doing the chain rule in order to give a better understanding.When you go deeper into differential calculus,you would be able to use the chain rule pretty fluently and would shorten the steps.

    • Jonathan Bryant 3 years ago

      @alex rider ah yeah I totally missed that (2) at the end thank you.

  • Fathima Raeesah 3 years ago

    She’s so pretty

  • sakil sazzad joy 3 years ago

    “time is the one thing you can never get back” thank you

  • bunny balaj 3 years ago

    youe method is very nice….

  • M G 3 years ago

    Sometimes I wonder what the backstory is she held captive in that white room? & her handler comes every so often when they need to make a math video? tosses her a cheeze it and VAMANOS? Hmmm I wonder… @ 5:35 her stomach is growling..MAYBE she does not get cheeze its afterall!! *GASP*

  • Moe Kiyam 3 years ago

    8:51… why arent we finding the derivative of the function again since we arent done? Shouldnt we be multiplying by 2?

  • t h 3 years ago

    does she have the write down the reflected version when she is making these videos?

    • Veritas et Aequitas 3 years ago

      No… She’s writijg right handed and the video is flipped

    • t h 3 years ago

      Uncomfortable Truth oh that makes sense, thanks

  • current_interest 3 years ago

    I didn’t know the chain rule was so … Hot!

  • i believe 3 years ago


  • Kian Hk 3 years ago

    to god hasti

  • Mad Map 3 years ago

    I wish you could be my maths teacher I would never bunk any of your lecture

  • only heart song only heart song 3 years ago

    You are sexy

  • Medical Art 3 years ago

    Nice video Gal Gadot

  • Premjith Premlal 3 years ago

    thank you 🙂 any CMA students here?

  • Vaiebhav Patil 3 years ago

    I never thought I would fall in love with a teacher 😍

    • beverly francis 3 years ago

      Stop ogling!

    • Vaiebhav Patil 3 years ago

      @beverly francis I’m NoT OGLing, I’m appreciating beauty

  • Vaiebhav Patil 3 years ago

    I’m Soon gonna fall in love with maths

  • Zamir Kazmi 3 years ago

    Great explanation

  • Crystalluna 3 years ago

    Did I just understood ? 😱
    thank you so so much 😭😭😭

  • Prince Helinsburg 3 years ago

    one thing i love about Nancy, is that she simplified math esp calculus i am a kenyan who feared math but now i can tacle hard looking math i now love maths thanx nancy

  • Abhishek Pinjarkar 3 years ago

    It was very helpful. Thank you

  • Music is life 3 years ago

    Bella e brava!

  • Ken Toby 3 years ago

    Thank you soo much

  • Really Virtual 3 years ago

    Damn – Nancy writes better backwards than I do forwards! The fact she can also read it backwards whilst explaining the concepts…. Mind blown!

  • Ravi Vishawakarma 3 years ago

    Thanks for making this math video

  • azeez notes 3 years ago

    “You don’t have to like math but You can Like my video”. I hire You Madam to do the Sales For Me.

  • Sterling Walsh 3 years ago

    Do you write backwards on that board so we see your work normally??

  • Saintsfan019 3 years ago

    You truly are legendary. Great teacher

  • Wilma Martell 3 years ago

    #finalsgang …. anyone else?

  • Jake Lopez 3 years ago

    Chain rule is my friend

  • 作井观天 3 years ago

    Excuse me, can you tell me what board are you using? It is so great!

  • YAHYE Ali 3 years ago

    Wow youre amazing nancy thank you for helping us i really feel intrested and confident thanks again 🙏🙏🙏🙏

  • Peter Gwanda 3 years ago

    🙌i feel like i have prepared enough for my exams this semister after watching nancy’s videos …may God bless you🙏

  • Paul Brewerton 3 years ago

    @15:00 how come you have -4 (1+cos 2x) sin 2x ?? Why is it not 4(1+cos 2x) (-sin 2x) ??

  • Zahra Jawad 3 years ago

    You’re amazing💛thx

  • Sona Sunny 3 years ago

    my exam is tomorrow..Where the hell i have been this long..finally kinda liking maths..what took u so long Nancy. You are really a life saver. THANKS FROM HEART

  • Senaxion Aria 3 years ago

    What kind of sorcery is this… how did she wrote that?

  • Alicia Zitouni 3 years ago

    i love you queen <333333

  • Renu Agarwal 3 years ago

    mam u are very cute

    • Frédéric Chopin 3 years ago

      Renu Agarwal mam please go and shit on the streets you fkin indian creep

  • Dranoc 3 years ago

    Best explanation I’ve watched. Thanks!

  • lydia hardy 3 years ago

    I wonder if she right or left handed

  • Mitanshu Sharma 3 years ago


  • Big_Evil97 3 years ago

    Thank you miss 🙏🏼

  • Joshua van Tilburgh 3 years ago

    I think it would be helpful to show why you don’t need to do anything else if you just have x in the parenthesis by just mentioning that the derivative of x is 1 anyway. You can still use the chain rule here, but obviously you’ll quickly learn that you’re done after the first step.

  • Sophy Heang 3 years ago

    teacher can make a video about Taylor series ?

  • Priyanka Medhi 3 years ago

    Wrong answer

    • Frédéric Chopin 3 years ago

      Priyanka Medhi your mom

    • Priyanka Medhi 3 years ago

      @Frédéric Chopin what ??

  • SequinBrain 3 years ago

    I like the not looking at notes to write equations. I need that skill.

  • Harry Goolnik 3 years ago

    I’m supposed to be revising maths but all I can think about is how she’s writing on the board. Do you write backwards!?!?

    • Babaji Roaster 3 years ago

      Yup me too. Lol

  • juan lyn ching 3 years ago


  • Muhammad Iffirdaus Ahmad Zailani 3 years ago

    Thanksssss i love you..🥰🥰🥰

  • Impervious 3 years ago

    Is there even a single male viewer who actually clicked for the lecture?

    • Obito 3 years ago

      There was a lecture?

    • Aarohan Sharma 3 years ago


    • Aarohan Sharma 2 years ago

      Yes man…

  • Kevin Lind 3 years ago

    Thank you for the excellent content! It helped!

  • Obed Hamed 3 years ago

    She’s so beautiful

    • Frédéric Chopin 3 years ago

      Obed Hamed fkin creep

  • Obed Hamed 3 years ago

    Derivative 🤤

  • shuga q 3 years ago

    is there any one rule that can solve all derivatives

  • Obaida Zoghbi 3 years ago

    Please someone tell me when i should stop derivating

  • Marwan Hussein 3 years ago

    When you stop derivating ?

  • Leonard Wong 3 years ago

    I suck at maths….

  • John Vandersall 3 years ago

    you have solved the equation what is it applied to pray tell

  • victoria gregory 3 years ago

    all the way from Kenya, i love how you do it Nancy.thanks

  • Maja Bayhon 3 years ago

    Thanks for the wonderful vid. Now I can teach the chain rule w/ ease. And I’ll recommend my studs to watch your vids also. 😉

  • Shanti Ratha 3 years ago

    I thought you were writing on the camera 😅

  • Hassam Kayani 3 years ago

    hahahaha .mujy sab samj a gya is ko dakh k…..

  • Graphic World 3 years ago

    i’ll use the math you taught me to build a cloning machine, i’ll your DNA code and that’s it

  • xitrus VENOM 3 years ago

    Thanks a lot……

  • Mike Jouhari 3 years ago

    How lovely and Classy

  • Gio Gio 3 years ago

    Can I just marry you? jk

  • Micae Trần Quốc Bảo 3 years ago

    How to make video with text like you? please tutorial me,

  • Susan Joe 3 years ago

    Thanks bud

  • Shivank Pratap Singhal 3 years ago

    Maths was never this interesting to me. You are lovely ‘nancy’!

  • WhiteChocolateMocha 3 years ago

    dy/dx = dy/du x. du/dx

  • zee 3 years ago

    wow i’m so gay

  • Anonymous being 3 years ago

    Damn you are hot🔥

  • Ziyad Riaz 3 years ago

    Ma’am i wont lie i never had any interest in calculus but after Wathcing yur vedio i jus feels like calculus is my thing i thank you very much for such a nice lecture may yu live long and keep on teaching us 😍😍

  • David Saari 3 years ago

    I was very embittered by your videos at one time, but it was not your fault and I am sorry for being verbally abusive! I have a very serious mental illness and I am just a bitter, poverty stricken 52 year old who lacks responsibility, compassion and respect! Your videos are very helpful to be honest and thank-you for helping me to study math to get my mind off of my problems! Have a nice day…

  • Julianne Buenaflor 3 years ago

  • Ahmed Awwad 3 years ago

    Chain rule ايه؟
    هاتي بوسة يا بت

  • Füñ By AI 3 years ago

    Damn! It is very difficult to concentrate on the board😩

  • M N 3 years ago

    Whenever I need to brush on a topic, I type eg “chain rule Nancy” and 💥.
    Thanks Nancy.

  • bc190404204 ABDUL REHMAN BUTT 3 years ago

    That’s the reason why people fail in Maths always, highering a female teacher with a beautiful voice and amazing figure with a gorgeous face how can someone focus on Derivative Result Fail… 😛

  • LIGHT YAGAMI 3 years ago

    if u were my teacher my attendance in school would be 100%

  • kigen peter 3 years ago

    Am in love and i now need a white woman to marry… seriuose no joke

  • Vernita Jones 3 years ago

    The double chain rule – is still left with a sin2x. How do you know whether to carry on with that or not?

  • Unknown 3 years ago

    Why do u look tired…

  • Molalign Alemnesh 3 years ago

    Hello dear lecturer I realy not understand you methods ,you should write on the board slowly , dont do machine fast

  • Abubakar Abdulrahman 3 years ago

    My Allah make me to be understand mathematics

  • samuel sam 3 years ago

    What of questions like x cubed (1 plus x) squared

  • samuel sam 3 years ago

    And also ( x-2/x)squared

  • NATRIUM Natrium 3 years ago

    I like the life lesson at the beginning, ;DDDDDD

  • Jennie Kim 3 years ago

    can you do more complex/longer problems? I get those small problems, but when it comes to the longer more complicated ones they get tricky.

  • kalpesh khare 3 years ago

    Hiee maam I’m from India……
    I like your teaching……….tnx……

  • Vedant SAKPAL 3 years ago

    miles better than eddie woo

  • Hammad khan 3 years ago

    any video for the differentiation of a trignometric functions????????

  • jewjew abrams 3 years ago

    A very wise physicst told me that introducing a bunch of rules is bad. He managed to teach me dervitives very quickly!

  • john redgs martin 3 years ago

    my concentration is distract to your beauty lol but i understand clearly

  • Paul Price 3 years ago

    I’m so dam stupid!

  • Paul Price 3 years ago

    What type of job would you actually use this form of math. Serious question?

  • Adam Walker 3 years ago

    how does she write infront of her the right way round, so we see it correctly. no matter how many videos i watch i dont get it, thats harder to figure out than the calculus…

  • DiveMarshall91 3 years ago

    Thank you NancyPi 🙂

  • Tim Brewer 3 years ago

    Nice video

  • Bleedingreen 3 years ago

    How to differentiate sin3x

  • MrCheeks 3 years ago

    Omg ur so hot

  • Tim omini 3 years ago

    I understood clearly

  • kraziibone1 3 years ago

    This was very useful, thank you!

  • SAMSON ONYANGO 3 years ago

    wow amazing NancyPi

  • reptilia5 3 years ago

    Why couldn’t my math teachers in school have been this gorgeous? I would have been another Einstein!

  • seanparsa4 3 years ago


  • Hope4NewDay 3 years ago

    “time is the one thing you can never get back”
    Well this shit just got real.

  • Sulman Albalawy 3 years ago

    ماشاء الله بنت جمييله شرح وينه ايام الجامعه تف عليك ي اسماعيل ابو قفه

  • Cel 3 years ago

    Thank you Nancy Pi for being so talented and smart, she can write backwards and teach me derivatives at the same time ughh 🥺❤️

  • beverly francis 3 years ago

    How can I learn to be left handed without misjudging and damage myself?

  • F Hedengren 3 years ago

    ‘the Chain Rule is your friend…’ brilliant!

  • James Bones 3 years ago

    your chain rule video beats the Khan academy intro to chain rule. thank you, good job

  • Joseph Dolejsi 3 years ago

    Why’s it negative 4 at the end?

  • Antonio Canuck 3 years ago

    Omg how can you memorize all that shit ?

  • Giulia Joe Assanti 3 years ago

    This was extremely helpful, and I am sooooo thankful!!!!

  • B.N Junior 3 years ago

    It’s been 3 years already since i watched Nancy’s videos.
    Thanks a million times. You made me love math. graduation bells about to ring💖. Just had to come back and say thanks.

  • Annie Marrie 3 years ago


  • Eimantas Vijaikis 3 years ago

    I only watch her videos because she is hot, i already know the math 😀

  • Tim Rubin Halcomb 3 years ago

    If you were my woman, I’d never use the CHAIN rule. I’d be to jealous. LOL GET IT? 🙂

  • Tim Rubin Halcomb 3 years ago

    y = sin(x^2). Let u = x^2. du/dx = 2x. dy/du = Cos(u). (dy/du)(du/dx) = 2xCos(u) = 2xCos(x^2)

  • 99T 3 years ago

    turned it into a philosophy lesson real quick

  • Michaela and Vincent 3 years ago

    Get this comment to 1,000 likes for a behind the scene video !!! BTW, Nancy, you’re the absolute best !!

  • Howawwe 3 years ago

    wow, i know have a bettur understanding of the chain rule u wifey material

  • Stefana Cioc 3 years ago

    marry me, sweet teacher!

  • enriko enrike 3 years ago

    I m more intrigued to the way you write on that glass than what you explained! You certainly are unique!

  • Jc Ramos 3 years ago


  • I’m here to help 3 years ago

    You seriously write backwards?

  • Sabrina Islam 3 years ago

    Just use substitution.

  • Bimboy Broa 3 years ago

    excellent teacher!!!! God Bless you Miss Beautiful. i learn a lot

  • Pang Vang 3 years ago

    this is quality content

  • lefa sesupo 3 years ago

    You have make my calculus concepts so easy for me Nancy.

  • Ayanfe-Oluwa Idowu 3 years ago

    Thank you for this vid. What I don’t understand is why there’s no need to take the derivative of (1+ cos(2x) ). cos(2x) is a composed function, so can’t we apply the chain rule three times, to break it down? Also, I’m afraid I do not understand how you moved from -sin(2x) to 2. Thank you so much for all the help you provide!

  • Shawn Pham 3 years ago

    so helpful, thank you

  • Koh Yandar 3 years ago

    Does she have dyslexia? How does she write like that

  • Wagner Matsushita 3 years ago

    I do like math, but you make it even more enjoyable! Thank you and keep up the good work

  • Jared Baum 3 years ago

    I too am a lefty that loves math. Want to go out?

    • Aarohan Sharma 2 years ago

      R u an MIT graduate?

  • Gear HD 3 years ago

    How do you film like that?

  • metalrave 3 years ago

    Taking Calculus online for school and my E-Text referenced this video.

    Very well done on their part
    Explained well

  • ᴀʟɪsʜᴀ 3 years ago

    This video was so helpful! I was struggling to understand this

  • Rehad Mohammad 3 years ago

    Thanks for videos such as this… I was practicing this topic and had to do some revisions and it helped a lot.
    Once again, thanks! 🙂

  • Expired glass 3 years ago

    Thank you soo much!! You saved my butt 😅♡♡

  • Abemelech Asclepius 3 years ago

    She’s left-handed 🤚

  • Tuwshinjargal Nasanbilegt 3 years ago

    Thank you Nancy ❤️

  • Daniel Kim 3 years ago

    you are a life saver

  • Yashraj Singh 3 years ago

    Awesome explaination Ma’am 🥰🥰🥰🥰🥰🥰

  • Elior Malul 3 years ago

    Nancy you’re a star.

  • Wendel Fabian Chinsamy 3 years ago

    Excellent job! The only explanation that helped me get it! Your videos are helping me immensely.

  • Niceakoto Umurerwa 3 years ago

    My crush ,good job

  • Francis El Profe 3 years ago

    Excelente Nancy.
    Very Good

  • Rosé Mohammed 3 years ago

    I understand it very well
    Thanks so much for this

  • Arnav DC 3 years ago


  • Arnav DC 3 years ago

    woah wait whats happening ur writing on the screen backwards or its showing us flipped … lol this is funnny

  • Luke Gordon 3 years ago

    Thank you Nancy – you are incredibly gifted

  • Usama rafieck 3 years ago

    How is precalculus different from calculus?

  • Kevin Brooks 3 years ago

    You’re gorgeous and sweet

  • Vishnu Raghavan 3 years ago

    “Zeit ist das Einzige, was man niemals zurückbekommen kann” Trotzdem habe ich fast ein Semester ohne dich Mathematik studiert …

  • Michael Jetnikoff 3 years ago

    Hi,chain broken,thee be free,here,thanx,bliss, XAMichael XAMBUNJILOM

  • Diarla Amaral 3 years ago

    WOW! You are amazing! Thank you so much.

  • Fahim Islam 3 years ago

    I’m really confused by whether she’s writing backwards on the glass cause if not, how are the letters not looking flippedddd??????????????

  • Tom Scott 3 years ago

    NP, so i notice you write almost exclusively in hi-speed mode, other than when drawing simple “=” or “( )” symbols and the like. is that because you are really behind the screen and would have to write backwards, or are you employing some black-magic trickery that i’m unaware of?? 🙂

  • Marissa Wilson 3 years ago

    Thank you! I appreciate your thoroughness.

  • Jerry PEAL 3 years ago

    I still don’t need to learn this , but………….

  • Patson Damascus 3 years ago

    great explanation

  • Patson Damascus 3 years ago

    beauty with brains

  • Yazmin Gutierrez 3 years ago

    Honestly that intro … *“and time is the one thing you could never get back”* drove me into my yearly call for action, outside the abyss of existential dread my mind loves to ponder. So consumed calculating my next moves I became standstill. . . Crazy how seemingly simplistic life sayings tend to hold such strong valuable life lessons that aren’t truly appreciated until life demonstrates its intricate multiple leveled dynamics in regards its importance throughout the course of our existence 😐

    • Alessio Xu 3 years ago

      Hummm mm bro i feel ya

    • Aarohan Sharma 2 years ago

      Someone isn’t paying attention to the video

  • jacob marsh 3 years ago

    thank you so much.

  • Adityabarno Basu 3 years ago

    Really made my concept crystal clear when to use and how to use the chain rule.I really appreciate your efforts.

  • Augusta Yarteh 3 years ago

    I did Multiply the power First with the y coficent. I am not clear with it well. I think your explanation is good for me and well understandable. Thanks a lot Nancy You tube is helping me greatly to work on my pre calcuse class even though I never took it to my former college never Well You tube is playing great role into my life and brain to understand all those work and all those functions. Thanks once more again miss Nancy. I am still trying to work on it.

  • Abbe Satty 3 years ago

    6:11 She said YES!

  • Kaylee yoong 3 years ago

    how does she write backwards

  • snory1736 3 years ago

    is she writing backwards….

  • Александр К 3 years ago

    oh I’m inlove…with calculus of course

  • Urvesh chilhate 3 years ago

    you look cute😅😅😅

  • Ali Özgül 3 years ago

    Nice lesson, more thanks. This times I work on chain rules for derivative of complex functions. Best regards.

  • 2Truth4Liberty 3 years ago

    2 + 2 = I’d like to be with you

  • Harshil Katira 3 years ago

    Everyone-Emily or Cinnamon?
    Me-Chain rule or no chain rule

  • Thomas William 3 years ago

    Super nancy thanks from Germany

  • Ritik raj 3 years ago

    Thanking you for the great help from India 🥺🤗

  • Stefan Pratarelli 3 years ago


  • Rayleigh San 3 years ago

    Thank you for your help 🙂

  • Jereely Lopez Hernandez 3 years ago

    It is my 100 perfect score for calculus

  • Jereely Lopez Hernandez 3 years ago

    I love chain rule find dy/ dx
    Y = ( 3x+1) and exponent of 7. What is chain rule with this find the derivative of ( 3x+1) and exponent of 7
    —— = 7 ( 3x+1) with exponent of 7
    This a derivative
    ____ the exponent was
    Dx was called derivative this is was its look 7 ( 3x+1)six -(3)
    —–7 ( 3x+1)six- (3)
    Were using multiplication 7×3=21 you cant change this form just copied
    —- = 21 ( 3x+1)six

    Exponent always addition
    X squareor dis(x2) 1x+1x= is x squared even of more.
    Its me je from marikina.

  • ayoub 3 years ago


  • Will Matos 3 years ago

    asmr + math!

  • Snigdha Sood 3 years ago

    didnt understand double chain rule

  • PARTH 4435 3 years ago

    Nice teaching…

  • Anuj Kantharajapur 3 years ago

    I don’t watch these vids for the math

  • Megan Wing 3 years ago

    This helps so much during online learning because of COVID-19 🙂

  • Akinyemi Adu 3 years ago

    Nancy, weldone. The video was and is very simple to understand. My students found it really interesting and liked it, meaning that its helpful. Thank you.

  • Tim Rubin Halcomb 3 years ago

    If you had a way to change time in such a way that the horrible things in this world would just disappear, then would you do it?
    I would.

  • Rishav Verma 3 years ago

    oh my god,, yau writes on the wrong side, with left hand🤔🤔

  • kapil kumarsingh 3 years ago

    1. After Find the slope (derivative)
    What do you want to achieve
    2.Use of slope

  • Soofia Khan 3 years ago

    How can you be so intelligent and pretty at the same time?…..Well, I’m jealous………….Love from India….

  • Adarsh Yadav 3 years ago

    Reason to watch her video ~nice explanation
    No there is another !

  • EyeZac 3 years ago

    how do you write backwards? (left-handed too!)

  • Alexandra Kaidan 3 years ago

    Are you? Mslm?

  • Abhranil Roy Roy 3 years ago

    Thnx Nancy I was wondering would I even learn chain rule ever even my Indian profs couldn’t put it this lucidly thnx again

  • Abhranil Roy Roy 3 years ago

    By the way what is”In5x”

  • Kaitlyn D. 3 years ago

    you explained this so well, thank you nancy!

  • Jackson 3 years ago

    I would more precisely define what outside and inside can be and is.

  • Ali Al Darorah 3 years ago

    The best teacher I have seen 🌹

  • Shahroz khalid 3 years ago

    Find the hypotenuse of right angled triangle whose sides are 6.03 and 7.96 … use the chain rule for function of two variables ….. Madam can you help me with the solution of this question?

  • dozzy C 3 years ago

    Hi Nancy, how do you write on the screen?

  • Don Faryar Ghara 3 years ago

    thank you!

  • SeeAndDreamify 3 years ago

    Thank you! This is the first I’ve seen of you and this was really easy to follow and understand. I’ll find some more of your videos now.

  • Aran_Ace 23 3 years ago

    You have saved my ass so many times, thank you

  • pervious chil 3 years ago

    I’d go to class ever day if she was my lecturer .

  • Shwetank Chaudhary 3 years ago

    So we need a MIT Grad …. for just “a chain rule” . It’s Funny . You are Funny and your audience is funny …

  • Shwetank Chaudhary 3 years ago

    After MIT what will i Do…….. i will make a video on chain rule …LMAO…XD

  • Gianne Badilla 3 years ago

    Hi… Umm.. can you please explain how (-sin2x)(2) turned just into sin2x and why the 2 in front turned to -4? I’d really appreciate it

  • Aryan NSH 3 years ago

    Thanks a lot! Really helpful! U are a good teacher 😄😄😄

  • Rohitashva Singh Rathore 3 years ago

    How does that text thing on mirror work?

  • Baobaomeow 3 years ago

    I have a final exam for my Saturday math school, and I’ve been just watching your videos to review. I really want to thank you from my heart. 🙂

  • M-0385-07 YUVRAJ N RATHI 3 years ago

    The pink highlighter is kinda soothing and satisfying

  • adrian lalo 3 years ago

    “you don’t have to like math, but you can like my vid” I already did that at the begging of the vid

  • Harsh Ranjit Shelke 3 years ago

    Hi Nancy.

  • Pragati Warhade 3 years ago

    Hey Nancy lovers let’s send Nancy our love…. Just add a comment by typing
    *LOVE FROM your country name here*
    As I m sending my love ….👇

  • Randa Putra Jusmal Melato 3 years ago

    i am here in 2020 and keep watching her smile.

  • shamim howlader 3 years ago

    I love this video

  • Uday shankar Misra 3 years ago

    Really you switched my mind

  • Salient Solution 3 years ago

    Is there a reason on number 2 that you don’t need to simplify it fully like the first example?

  • Hiral Patel 3 years ago

    Looking beautiful

  • Bonolo Nkopodi 3 years ago

    Please help with derivative of tric🙏your explanation is super❤!

  • Arul Kumar 3 years ago

    Mam this is my request please make
    Subtitles for our good understanding

  • Blah123 3 years ago

    Wow you are really good at writing backwards , it even looks better than my handwriting when I write forwards!

  • nithish chandra 3 years ago

    i think its deravite of x^n = n*X^(n-1) –>x to ax+constant –> a*(ax+constant) its bit confusing

  • nithish chandra 3 years ago

    chain rule is for double functions of respective derivative .thanks for informative video

  • groovychick 3 years ago

    Shes so good at writing backwards

  • Aayush Behura 3 years ago

    Thank you very much,I was struggling in this chain rule wish we had teachers like you.

    Love from India.

  • Alex 3 years ago

    Awesome explanation, easy to understand.

  • YOGESH BHATI 3 years ago

    Dear Nancy
    At 8:48 , Answer can be (18x+45)(x^2+5x-6) ^8.

  • Uday shankar Misra 3 years ago

    Plz give the concept of sin ²x+cos it=π

  • Martin Lopez 3 years ago

    thank u nancipy

  • Basil Kapeta Tembo 2 years ago

    Nancy may you please make a video on partial and complete defferention

  • Basil Kapeta Tembo 2 years ago

    Rather defferentiation

  • Miaulin K 2 years ago

    That was a great transition into the “like and subscribe” thing! Also, excellent video! My calculus book is long and complicated and doesn’t provide good examples, but this cleared it all up!

  • Brajendra Pandey 2 years ago

    It feels weird when you write on that glass; the glass is so clear that it feels you are writing in the air.

  • Ashley Melbourne 2 years ago

    Hi Nancy. Can you help me in solving this using chain rule? It would be a big help. I just can’t solve these 😭

    1. √lnx(x)-√1+ln(x)
    2. √√1-sin(x) + sinx

  • Tambuwal Maths Class 2 years ago

    Keep on the good work

  • Mario Silva 2 years ago

    It is fantastic when persons like you, have a pleasure to help others, the sounds of your voice sounds like music, has charm to teaching, thanks a lot!.

  • Feta Chea 2 years ago

    You are just the best!
    Thank you so much!

  • LolzChannel 2 years ago

    Thx so much! Teacher is teaching for hours and hours and I can’t focus because it takes tooo long. This short video gave me more information than her!

  • MATHS CLASS Pawan kumawat sir 2 years ago

    Hello friends
    Maths Class Pawan Kumawat Sir

  • Pietro De Nicola 2 years ago

    Tecnically you always use the chain rule. It’s just that the derivative of the inside may be 1.

  • Frank Josh 2 years ago

    Grately is just Wooo

  • Don Mcrapsavier 2 years ago

    6614931481 comment allez vous MADAM

  • Jaish 478 2 years ago

    perfection speaks itself

  • VoiceCrackJack 2 years ago

    Thank you, this helped a lot!!

  • qtz. 2 years ago

    5:36 somebodys hungry huh hahaha

  • Abhishek Singh 2 years ago

    Thanx nancy Gotta feels like I am again studying maths you really helped me a lot I was a maths nerd one year before. your videos are like life saver for me so I think to give you big thanx just bcoz of you I did best in my final exam of college and now I got a job in Microsoft in California as a data scientist you make my life

  • Abhishek Singh 2 years ago

    You are so talented. Keep it up

  • Anwaar Anjum 2 years ago

    Your expressions eye contact each nd everything is pretty and perfect dear Nancy..

  • lukas graumans 2 years ago

    lucky americans y’all have a choice if you take calculus or not

  • PoorManRC 2 years ago

    After 3 Videos of yours, I feel like I’ve learned MORE than in an entire Semester!!
    I’m also staggered by how you write SO well, BACKWARDS!! 😲

  • Shivam 2 years ago

    I am professor in college and don’t know what I am doing here

  • Pindi Phobia 2 years ago

    make a video on Normalization

  • Physics Anthony 2 years ago

    Your teaching style is really amazing

  • ample 2 years ago


  • Sira AKA Sims Bradakhi 2 years ago

    Stop lying to us Nancy😁
    You’re the best teacher ever🤞🏿

  • SAJEK 2 years ago

    Now, I love calculus more because of you.

  • Sendini Randeniya 2 years ago

    Is she writing backwards on a glass ???? Guys, I’m so confused ?!?!?!?!?! 🤔

  • Vaibhav Kumar 2 years ago

    Getting bored in lockdown

  • Lily Walsh 2 years ago

    I thank God the day I came across your channel. I love how you make these things look so easy. Thank you Nancy ❤️. You are a truly amazing teacher

  • Grant Martin 2 years ago

    Marry me

  • vk 180 2 years ago

    hello madam iam from kerala (india ) your videos help me a lot thank you miss

  • Oh Wow 2 years ago

    9:41 i think I’ve heard that line before but not from this tube…

  • Dan’s Detailing 2 years ago

    Thank you so much 🙂

  • Muong Kimhong 2 years ago

    my physic professor came with 1 marker and write bunch of physic formula and then left.

  • kaiser poblete 2 years ago

    This is good and shit she’s hot.

  • Keys 9914 2 years ago


  • Ayna Shah 2 years ago

    Gotta say, she’s pretty amazing.

  • Pharung Awungshi 2 years ago

    Thanks for uploading. it’s worth watching

  • Hitler was right. 2 years ago

    For the last problem. Shouldn’t it be positive 4? in 2(1+cos2x)(-sin2x)(2) and not -4 since your multiplying by two positive 2s…..

  • Abhay 2 years ago

    Don’t fall for her whenever she says it’s the last type of derivative.
    You have to watch the whole video.

  • Krrish Kumar 2 years ago

    I never believed that beutiful people could do Math😂

Comments are closed.