MIT grad shows how to find the derivative using the Power Rule, one of the derivative rules in calculus. It is a shortcut for taking derivatives of polynomial functions with powers of x. To skip ahead: 1) For HOW and WHEN to use the power rule, skip to time 0:22. 2) For how to use the power rule when you have a FRACTIONAL or NEGATIVE POWER, skip to 5:22. For my video on the other differentiation rules, PRODUCT RULE and QUOTIENT RULE, skip to https://youtu.be/QqF3i1pnyzU?t=456 Nancy formerly of mathbff explains the steps:

For how to differentiate using the formal LIMIT DEFINITION of the derivative instead, jump to https://youtu.be/-ktrtzYVk_I?t=628

Support Nancy on Patreon: https://www.patreon.com/nancypi

Follow Nancy on Instagram: https://instagram.com/nancypi

Follow Nancy on Twitter: https://twitter.com/nancypi

HOW and WHEN to use the POWER RULE: If the given equation is a polynomial, or just a power of x, then you can use the Power Rule. For a term that's just a power of x, such as x^4, you can get the derivative by bringing down the power to the front of the term as a coefficient and decreasing the x power by 1. For example, for x^4, the derivative is 4x^3. If you have many terms added or subtracted together, and if they are powers of x, you can use the Power Rule on each term (by the Sum and Difference Rules).

NOTE: The derivative of a constant, just a number, is always 0 (that is the Constant Rule). Also, if you have a term that is a constant multiplied in the front of the term, like 2x^3, you can keep the constant and differentiate the rest of the term (Constant Multiple Rule). In this example, you keep the 2 and take the derivative of x^3, which is 3x^2, so the derivative of the term 2x^3 is 2*3x^2, or 6x^2.

ANOTHER NOTE: You can use the same power rule method for fractional or negative powers, but be careful... for negative powers, it works as long as x is not 0, and for fractional/rational powers, if the power is less than 1, your derivative won't be defined at x = 0.

The derivative is a function that gives you the instantaneous rate of change at each point of another function. You can calculate the derivative with the definition of the derivative (using the limit, see https://youtu.be/-ktrtzYVk_I?t=628), but the fastest way to find the derivative is with shortcuts such as the Power Rule, Product Rule, and Quotient Rule.

For my video on the CHAIN RULE for finding derivatives, jump to https://youtu.be/H-ybCx8gt-8

For more math help and videos, check out: http://nancypi.com

Editor: Miriam Nielsen of zentouro

https://www.youtube.com/zentouro

Director: Kristopher Knight

https://kristopherknight.com

hOw iS ShE wRiTiNg bAcKwArDs

i think it is supernatural powers

She graduated from MIT…she can do anything man….haha…..OR….you can just turn your monitor 180 degrees and it’s no longer backwards….see how smart I am….oops not too smart…now I can’t see beautiful Nancy Pi…haha

@MisterGreenGuy Guessing she’s right-handed as well.

Because science…

See, he had evil parents who though they were funny and only taught her to write backwards! Now she is incapable of writing forwards and this is her only career option!

MIT copied your technique.

plzzz make a video of finding domain and range on a graph and with the brackets/ parentheses

Farthuse Akhter she already made the video on how to find the range and domain for function f(x).

Good vid as always Miss Nancy 😊

Wow she is sexy and intelligent.

Aaron Perez I had you at sexy

Ok Boomer

I’m learning about derivatives right now , this video was quite helpful

its hard to be you self to a non biological entity ,like a camera, relax your literally like 1000% cute ,,,love the hair

I don’t even need to know math and I’m not in school or anything but I still come to these vids

Xueq same!

Xueq tf how old r u

@Im Legit 22

Thanks are you going to put all your lectures on DVD for purchase?

Say something stupid like that again watch your ass be in depth ,she helps from her Heart

What’s a derivative?

Where were you in the beginning of the semester 😭😭😭

One word , clusterfuck .

Dangit I took my finals before this video uploaded

Just in time for my calculus final tomorrow!😍 I love you!

David if you don’t know the power rule by the time your calc final rolls around you’re really in trouble

So, how did it go?

@David you’ve failed.

Hello Nancy;

I’m Prof. Cris from the Matelok Channel. A pleasure to always watch your videos .. I really like your style of making the videos .. Do you use a glass or something like that? …

MARRY ME

I’m totally not involved in this

Nancy video! I’ll still watch even tho my exams finished yesterday haha

The power rule also works on constants! Think of a constant as being multiplied by the zeroth power of x, so that on taking the derivative, the zero is pulled down and the whole term disappears. (Not that there’s a reason to use it but it’s always good to see mathematical rules staying consistent.)

You are right

constant lives dont matter!

Well done, Nancy. Keep up the great work. Proud of you

Will you marry me 🍸💎💍

Collab with Hannah Fry?

How to do the “Summation of” thing… You know, the giant “E” thing?

Crap, she probably won’t see this.

NANCYYYY!! You are a damn goddess.

The world should be saying “subscribed to NancyPi”

I don’t care about the other pies on YouTube. And I don’t even math anymore but I still watch your films… I should have said videos.

How write sooo

Can you help me with the fundamental theorem of algebra and complex zeros I have final exam 😭😰

They Said Maths is Beautiful, Man they Really Meant it 🙂

Nancy The Math Saviour

At the beginning of the video, you can see the updated look of her today. Look really good!

Nancy, thanks for your teaching!.

Can you help find the range

Nice 😊

I ❤ you Nancy

Ok, guy who has not done this maths for … a while shall we say. What the heck is a derivative? And why is that useful?

You should start here

Please more derivative videos! Thanks :))

She is so cute)

Angel Nancy,

Thanks for teaching me Power Rule.

Please make videos for the following topics:

How to find Maxima,minima and points of inflexion by using Differentiation.

HAVE A NICE DAY!

if u were my math teacher 100/100 in exam is 100% guaranteed

Nancy, I managed to do that in my head in about 2 seconds. But listening to you talk it through took my mind of off Brexit for a few minutes. All the best from England, and Merry Christmas.

Just helped me pass calculus the other day! (That U-Substitution video saved me xD) Thanks Nancy!

thank u

guys – she is not writing backwards….just want to put that out there.

Can you do partial fractions integration?

Can you make a video on linear programming

Calculus is 2 quarters away but hey this shit’s interesting and she makes it sound easy

I really don’t need this lesson I’m not in school but I still watch because of you <3

I graduated and I still watch your videos

your awesome. just saying ;]

Works like Magic ✨🎩✨

Your beauty is pi, it never ends

Your comment is irrational.

😀

NancePi can you tell me how you got/built your “lightboard”? I am in the process of this at my university. Any help would be great. PS – your videos are very helpful.

Also my email is bill.arbuckle@oc.edu

❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️

so well explained. made life a lot easier! thanks!

It’s good to have you back Nancy

I have a suggestion. You should do a quick review to make sure we’re all on the same page. In fact you should do it with my problem set which i need to finish by Thursday. I’m only half kidding strange beautiful internet math lady.

You are so beautiful and I love to learn maths from you …

Thats my babyy

Merry Christmas 🎄🎄Nancy. Thank you for great creative math lesson.

She’s so sexy

Hi Nancy I hate to blow your trick but I believe you are not writing backwards 🤔you are flipping the video horizontal 😬 ps I have a total mind blank with math it may be a form of dyslexia as it has been the hinderance to my career all my life 🙁 your channel is just very soothing to the ears and eyes 😳😂

yo nancy

Does anyone else spend 95% of the video staring at Nancy?

she looks like fran from star gate Atlantis

who doesnt

Yup

no

sometimes she smiles as if she was explaining naughty things, init?

i love pasta

Hey Nancy, it would be great if you could do more calculus for the near future. You saved me from Algebra last semester and I’m gonna be taking Calculus next. Just a suggestion if you’re not sure what to do 🙂 Love your vids! High quality all in all

O

Great job on your videos nancy thank,s

Do you do differential equation? that stuff is hard to swallow

You seriously taught me what my teacher didn’t, not only that but your very pleasing for the eyes

I just wanted to take the time to say thank you because you helped me soooooooooooo much throughout the years!! I just took my last college lvl math class at UMD and I passed with a 92% thanks for uploading these videos to youtube when you don’t have to. It really helps alot of us out who may not have the best of teachers or the learning environment for math at some colleges just isn’t personal enough.Anyways you helped me more than you can imagine, so thanks again.

Hi Nancy, can you please do a video on ln and e? Thanks

she does ln in her logarithm video and 3blue1brown has a great video on where e comes from to tide you over until nancy does one of her own.

The ending is the cutest thing ever! hahaaa nice job

Decaf-Math ASMR bro it’s math, what’s cute about it😐

Tap tap like

🙂

please do related rates… its urgent lol

your videos help a lot thank you.

Finally I fell in love. Marry me

So envious of your editing skills 💯

Thank you very much…I understand you …I am a techer of math …I think you are the princess of girl who teach math …can I now you e mail please…

I found this channel by looking at a YouTube profile of a guy who claims to be an alien. I don’t understand any of this but holy cow your a beaut!! ( sorry I’m sure you hear that too much). Just passing through c ya!

happy new year nancy

Hey @NancyPi, You’ve mentioned that you were also highly interested in computer science in high school, right? Did that continue into college? I recently watched lectures from MIT on general computer science (using python). It was extremely helpful and the internet is blessed to be able to have access to such high quality and free educational materials.

In future videos could you expand upon the material already provided by MIT? More intermediate and advance topics of computer science… and since you’re a self proclaimed math nerd, you could focus on algorithms and how they work (instead of how to implement them). You could do a video on gradient descent as an example or any of the many sorting methods and the maths behind them.

Another suggestion would to be to take a page from the youtube channel “Socratica” and provide short clips on studying techniques, job/internship hunting/interview techniques, and anything else that helped you get through MIT’s rigorous curricula. This would help increase your upload frequency, while not taking up too much of your time that is normally spent on your longer videos.

Nancy I fell on love with you

You like that huh

Nancy, I do not know how many people who watch you realize that you are teaching extemporaneously and to an extremely wide audience. This shows your grasp of the subject matter and your grasp of how to speak to people about complex subjects without talking down to them and without talking over them. It is obvious to me that you are a disciplined person who cares about others. A rare and desirable set of character traits.

Please explain compound function, composite function, inverse function and one-to-one function in the next video. Thanks

How is it possible that some book has mathematically balanced letters on all 604 pages?

This book is called the Qur’an and I believe it is the only book in the world of this kind…

And how can this really happen in a book that is believed to be revealed by God, how can this be a coincidence?

It should be interesting for every mathematician…

I like watching your math tutorials you are a good tutor. Your explanation is very clear and easy to listen to. And I think you have a little giggle in your voice when you throw in a new concept which makes me giggly too.

why am I watching videos about things I don’t need to learn

Can you do a video on the law of sin and cos

the reason ,guys, that you don’t see a ring on it yet is because…..I’m going through some financial issues atm.

(edit) I “forgot” that she was a MIT graduate and decided I’ll just stay broke for awhile.

Thank you so much for posting these! They’re so helpful!

thanx Nancy!!

I passed college because of you. I owe you thousands.

She slays me with her beauty

You’re so pretty. You’ve transformed me in Math

Jesus Christ, you thirsty ass dudes on here are pathetic. Thanks for the sharing these shortcuts NancyPi. Great help!

nice work dear

Hi Nancy, Can you make a video explaining the rules of mathematics? For example, the coefficient of the unknown should not be negative or say the denominator if it is not relative

The power rule. Wow, been planning calculus videos on my own channel. I hope one day I’m able to adopt your production quality, it’s soo next level. Your channel is such an inspiration. Great work you’re doing here….. Keep it up Nancy

I just discovered your channel and I love your content and teaching style! Do you have plans to make videos on Series?

matrices next, please !!

Hello.

Can you please make a video on HOW TO FIND SOLUTIONS OF ORDINARY SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS.

It would be really helpful.

Lastly…your are very hard-working and dexterous.✌🏻

You should hit up Michel van biezen you guys would make a great couple

I really want to say u r hot n sizzling

updated videos! And you’re much more relaxed now. high five!

I need to use calc again and couldn’t find the mathBFF channel, I’m glad you’re still here. high five again!

who said that beauty and science do not mix !!??

Sorry cute girl you’re late I’m already an engineer 😢😢

Nanci can you do series, sequences and approximations video, pleade

More videos, please!

At the risk of appearing really stupid, can you really write backward so proficiently?

I just found your chain

interesting video

ps

you are beautiful

Hi Nancy, would you please make a video about Differential Equations? Please save my life for this semester……

Mam, you’re amazing. Thank you so much for such effort for us. #Pakistan

Nancy please teach us how to graph sin and cos

v.gooooooooooooooooooooooooooooood

Thank you so much for explaining these concepts in such a simple and fun manner.

can you PLEASE make a set of videos on statistics and probability? The topic is simply killing me and I sure could use some help.

By the way, I like how all the formulae appears right next to you on the screen 🙂

how can you write backwards so well

wanna get married

Could you please teach Fourier Transform or convolution? it would be awesome love ya

could i just ask, are you writing backwards on glass or something? the ffff

I like math, but I don’t like NancyPi. (Happy belated opposite day!)

can u teach vectors for a level cie

thankyou thankyou thankyou!

+NancyPi Hey Nancy just wanted to ask will ever be doing a video of quadratic inequalities/linear quadratics soon?

Hi Nancy thank you for your wisdom and for your cool teaching application, I was wondering do you have any videos about piecewise function and graphing, I loved to see you explain this thanks

No matter what you teach, your class attendance would be 170.7%

How the fuck does this girl write like this. From her perspective is she writing backwards?

Can you do videos on stats covering probabilities

Universal Repulsion – a new fundamental force.

Similar to universal gravitation force between matters, there is an universal repulsion force between line of sight electrons on the surface of matters. Without gravitation, we cannot orbit the Sun. Without repulsion, Sun light cannot reach us.

Because electrons are on the surface of all matters, and because line of sight electrons are constantly repelling each other with Coulomb’s force F=Ke x ee/R^2, therefore between the surfaces of matter A and matter B there exists an universal repulsion force F=Ke x aebe/R^2. In the equation, a is the number of line of sight electrons on the surface of mater A, b is the number of line of sight electrons on the surface of matter B, R is the average distance.

This universal repulsion force is always existing at any distance, therefore line of sight electrons are constantly connected by this force at any distance, therefore they can share their kinetic energy instantaneously at any distance.

This universal repulsion force is the conductor of light energy in the vacuum space between stars and planets. Light energy is instantly shared between line of sight vibrating electrons on the surface of the Sun and electrons on Earth outer atmosphere, then it becomes light wave and traveling in the air at light speed C.

This universal repulsion force is the conductor of light between things you see and your eyes. Due to air in between, light speed is C.

This universal repulsion force is the conductor of EM wave between antenna and receiver. Due to air in between, EM wave speed is C.

Due to the existence of universal repulsion force, all star lights reach Earth outer atmosphere instantly, become light wave traveling in the air at speed C.

Sun light takes 8 minutes to reach us is mistaken. Time delay in space communication is impossible.

If light speed in vacuum space is infinite, relativity, electromagnetism and quantum physics will be all wrong.

Use MIT trillion frame per second camera to measure light speed inside of a vacuum glass bottle, we can prove light speed in vacuum is infinite.

Light only exists in air, water, medium/matter. There is no light in vacuum space.

Energy instantly teleported from the Sun to Earth outer atmosphere. Due to the existence of universal repulsion force between electrons on the sun and our outer atmosphere.

Einstein and Newton thought light is something traveling through space at light speed. It has both wave and particle properties.

They were both wrong.

Make more calculus videos plz

I found a video from your channel thanks to recommended videos cuz I’ve watched many math/science videos – and wow, I love you and your videos! You explain everything so good, you write so good, and love those ‘speed-ups” and how it’s filmed/recorded. Wish I had your videos to watch when I had math in school, but as it is now – your videos are perfect to refresh the memory and I actually also learn some new stuff. You’re an amazing math teacher! BIG love to you ❤️❤️❤️❤️

A good role model for women. Thanks for the informative vids.

Love you, Nancy. Really helped!

Nancy you dont even need the cheat sheet front to back .

If this was my high school teacher… fuhhh💀

Thanks for this! You teach so much better than my professors!

My new math teacher .

u brought my interest back in math ..so please teach us engineering mathematics too…we r eager to watch ur video

I love NancyPi, I used to watch your previous channel. You’ve inspired me to start a YouTube channel to help my students learn maths, and for anyone else interested. Check it out. “Power rules” 😻👍

Plz make a video about Complex numbers I have an Exam about it next month

Please do piecewise functions equal and not equal to 0!!!

How’s life?

Why did you stop uploading? :/

my qus what is all natural numbers sum (1+2+3+4+……………..)

could you do a vid on Consecutive integers?

Hi Nancy, I’ve really enjoyed your content over the years and they’ve helped me tremendously thank you. I’m trying to refresh my memory since I’m about to start my final college math course. Do you know of any websites or books that I can use to practice each math lesson after I watch your video? Any help would be greatly appreciated.

Do exponential graphing and inequalities or finding the maxama and minima within a domain .

I’m not sure if people come here to learn maths or to see Nancy…

Kindly make a video on maxima and minima of function of two variable please solve this example

x^4+4x^2y^2-2x^2+2y^2-1

I must know how you animated the numbers on the board!!!

Leonardo da Vinci is proud of you.

Hi, please do a video on matrices

Doing these are actually fun lol. Math is a lot more fun, and intuitive, when you just take a step back and really try to understand it. Luckily, Nancy I here to save me in class and everyone!

This comment section is filled with thirst tweets and hilarious puns but. Nothing to do with math – I love it :p

She is so cute and thats why i am here mostly….

Absolutely I am in love. Marry Me 😍

thanks for sharing

Its so helpful 😊

I love your videos! Thank you! 😁

Chinese viewer has entered chat

Nancy you are such an inspiration! You inspired me to start off my own channel. Great job! Keep it up x

Hi Nancy! Thank you so much for all of your videos — you explain everything so well! Can you make videos on sequences and series? I really struggle with partial sums and pretty much all of the tests to determine convergence etc.. I feel like sequences and series are a tough topic across the board, so a series (ha) of videos on this topic would probably be helpful to a lot of us.

Hello Nancy. I have a big question : how is it possible to write in reverse like you’re doing in all your videos ?

I mean : you seem to be sited behind a glass and write letters and characters in inverted ? Or maybe there is a trick ?

Can you explain us how you realise this kind of video ? I’m beginning teaching to youtube too, and this way of presenting is very very cool !

Thanks Nancy! Helped a lot, currently my grade 9 math teacher is so bad at teaching me limits and derivates

This is why girls pass maths and boys fail because teachers are always male. My education would have been a lot smoother with a teacher like you.

No, that’s not why.

Love you ma’am thank you so much 🙏❤

a beauty doing math? so..when do we marry? i already know the date 🙂

very good tutorial but i have 1 question………………how do you write backwards like that???

Nancy! Can you please do a video covering Graphing Exponential Functions? Growth and Decay on a graph

you thirsty men under here are so creepy and crowd a space meant to seek help with useless pining. she doesn’t get paid enough to put up with your sh!t…..

I’m trying to learn *MOVE*

I am curious about how she wrote. It seems that there is a transparent glass whiteboard, on which she wrote, between the camera and her. However, if she stood on the other side of the glass whiteboard, then everything that she wrote would be reversed/mirror, which is very difficult for the writer. Did she really do that? But if she wrote normally, how to make the formulas mirror back in the video? After all, you can see that the formulas covered her left hand, which means she should be in the back.

Any ideas?

You’re the best maths teacher I’ve ever had…and I’ve studied fully at both a private and a grammar school. Keep it up! I recommend you to everyone 🙂

Used to hate boring generic looking math teachers. Now I understand their value.

Wow you’re amazing

Can you make a series of video about matrix 0 to 100?

Thanks a lot

Excellent video!!! Thank you very much! for all the videos. Saludos cordiales.

You’re an excellent teacher!! Hope you would write a book(s) with video solutions to accompany the examples. It’s not easy, I know, but just a suggestion.

Hi Nancy you are a saviour thanks a lot for your integral videos…💗

Do you write inverted or inverted all video on software? Pls answer, bc it is killing me.

Yes it did help a lot. Thank you.

If you didn’t do it already, plzzzzzzzzzzzzz do complex numbers plzzzzzzzzzzzz

NO WEDDING RING?? so ur tellin me there’s a chance…… 🙏

John Burgdorf lol

XD

I am an engineering major in college and you teaching has helped me alot in my journey but GOD DAMN!!! You got to be one of the most beautiful woman i have ever seen.

Nancy, yes I want to push that. You do a great job at teaching math!!!

Its summer vacation and I’m still watching

HI!

Can you solve the standard questions, from algebra , limit, integral

Actually this is mirror effect. Actually she is not writing right to left but this is the mirror effect. She is actually sitting left of her and right of us

Writing backwards is the impressive part.

And they said your just another math teacher.l don’t think so.😎 Stay real.

why the power becomes less 1 degree from the given power? please give me reason practically

Question: the constant “C” has rules ???

Beautiful😍 math!

Keep it up! Your the reason why I am smartest in elementary school! Edit! Videos are very well done 👍

Tip*** To minus one from a fraction, just keep the denominator on the bottom and for the top subtract the denominator from the numerator. Example 4/3-1 = 1/3

You are not only intelligent but BEAUTIFUL also….keep it up

ONLY THING I WANNA LEARN IS YOU’RE PHONE NUMBER

Who down votes her videos? Probably fat girls.

Nice video Wonder Woman

OG ASMR calc

Could you do a video on span, as in vector algebra ? ‘Cause of my short attention span when I watch your videos ….

Miss please come to India i will marry you

How do you write so good backwards!? 🤯🤯🤯

You are God’s gift to Calculus!! Thank you 🙂

Thank goodness for this video! I slogged through two hours of the original method for a 60%, but this makes it easy, and I never thought id say this, fun!

So beautiful😍💓 maam, 😊😊

i think im in love with you

Adorei o canal. Muito bom❤️

hii nancy mam ….where are you from???

im in 6th grade and i have to take advanced classes 🙁

achei seu quadro bacana!

nice mam

😍😍

Best explanation dear teacher lots of love from india😍😍😘😘😘

I wish i have a chance to meet u

Had she been my math teacher, I convinced I would have paid much closer attention in class.