Derivatives… What? (NancyPi)

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Published on September 6, 2018 by

MIT grad shows the DEFINITION of the derivative and how to FIND the derivative using that limit definition. To skip ahead: 1) For what the derivative MEANS, skip to 0:23. 2) For the SLOPE OF THE SECANT line, skip to 2:53. 3) For the SECANT BECOMING THE TANGENT and DEFINITION OF THE DERIVATIVE, skip to 5:54. 4) For how to FIND THE DERIVATIVE USING THE (LIMIT) DEFINITION of the derivative, skip to 10:28. Nancy formerly of MathBFF explains the steps.

For my video on the shorter, faster DERIVATIVE RULES for how to take a derivative, jump to: https://youtu.be/QqF3i1pnyzU

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

INTRODUCTION to derivatives:

1) WHAT IS THE DERIVATIVE? It's a function that tells you the slope (of the line tangent to the curve) at every point. Another way to think of it is that the derivative gives you the rate of change at any instant (the "instantaneous rate of change" at each point). You can find the derivative either with the proper DEFINITION OF THE DERIVATIVE ("by the limit process") or the faster, simpler way with the shortcut derivative rules such as the Power Rule, Product Rule, Quotient Rule, and Chain Rule. This video shows the first way, with the DEFINITION of the derivative, and how to use it to calculate the derivative.

2) SLOPE OF SECANT: To make the definition of the derivative, we can start with the slope of the straight secant line through a point x and some other point nearby, h distance away horizontally. If we label the two points and use the slope formula to write an expression for the slope of this secant line, the expression you get is [f(x+h) - f(x)] / h, which is also known as the DIFFERENCE QUOTIENT.

3) DEFINITION OF DERIVATIVE: That straight line slope we just found is actually a decent ESTIMATE for the slope at x, but it's not really the slope at x. We can get the EXACT slope of the tangent line at x by closing in on x and narrowing h to zero, by taking the LIMIT of the secant slope, as h approaches 0. The slope of the secant line becomes the slope of the tangent line. Not only is this limit equal to the slope of the tangent line, it is the definition of the derivative (when the limit exists) or f'(x).

4) HOW TO FIND THE DERIVATIVE OF A FUNCTION USING (LIMIT) DEFINITION: If you have to find the derivative "using the definition of the derivative" or "by the limit process", then you can use the limit definition we just found for any f(x) equation you're given. Remember that the f(x+h) part of the formula means to replace x with (x+h) anywhere x appears in the function f(x). If you want help knowing how to find the limit at the end, you can jump to my video "How to Find Any Limit": https://youtu.be/nJZm-zp639s

For an intro to the concept of limits, jump to: https://youtu.be/poBobcFn1Co

For more of my math videos for calculus, precalculus, and algebra, check out: http://nancypi.com

Category

Advertise here. Telegram, Signal - Call/message +1-868-308-4028.

• Thank you Ms

• 2nd comment

• Studying the mathematics section for my FE Civil exam. Thank you for this great explanation, best one Iโve ever seen!

• I don’t even like math. But I have problem no watching your video!

• Tharak aur sarak ki koi intiha nahe hote. Hahahaha

• You should be a math teacher if you already aren’t. You make topics so much easier

• swear to god, teachers make around 100k at my school

• What makes you say teachers don’t make enough? They make about \$30 an hour.

• @Bryan Parks As a teacher, I can tell you that is a lie.

• @Greg Angstadt-Williams how much do you make?

• @Andy Babay some professors dont either

• Not even in school but always enjoy your videos

• Good Nancy

• Awesome! We just started this in class this week.

• I have an integration doubt . Some people say that (sinx)^1/2 is integratable because the graph of the function exists so we can calculate the area under the graph but others clearly state away it’s non integratable. Help with this one. Please.@nancypi

• It’s non elementary, meaning it doesn’t have an antiderivative expressible in terms of elementary functions like trigonometric or exponential.
But it is integrable in the sense that you can find the area under the curve of the function, maybe through numerical methods, but the Fundamental Theorem of Calculus can’t be used.

• Hilbert Black so you can’t just find out its integral using common integration methods? Also can it be integrated under specific limits like example from 0 to pi/4 using definite integration properties?

• @Samik Saraswat Not as far as I can see, but check this thread

• Hilbert Black thanks

• Do you ever have the time to check out some of the math work by Eddie Woo? If a story is well told, learning may well flow …

• I like how you made the line change with your hand movements. Also ur awesome and very helpful ty so much!!!!

• Love you !

• Yay thanks I needed a quick review your awesome!

• Nancy, your math videos are good refreshers for our senior engineers, especially when dealing with complex transient problems. And several of our younger production employees are interested in engineering, and maybe pursuing engineering and your tutorials are an excellent means to motivate them. Thank you.

• Can u plz do a video on left hand limit and right hand limit…! Plz..plz..

• she covers it, in introduction to limits

• the way you teach is astoundingly clear i have come to see math in a new way thank you!!!!

• Could you cover topics in vector calculus and linear algebra?

• disaster, I guess thing ,,,,, in ones ,,,,,,,, provokes different emotions to each of us there was a new York tranny whom called him self Disaster the things put on tv for us to be assimilated to , after a while just for sanity we need maths

• Oblique asymptote please

• Omfg this is exactly the material I was looking for. We just went over this in class yesterday and I like to watch videos on what was covered in class to help with my studies… great timing ๐

• Really loving the new videos

• she can write backwards!

• NICE NICE NICE

• ‘Life is not that simple usually’ nice quote by you.

• Angel Nancy,
We know,
A Secant line always cuts / touches two points on a graph.
And,
A Tangent line always cuts / touches a single point on a graph.
Therefore the Secant line will never touch / meet the Tangent line on a point of a graph.
Conclusion :
Differentiation fails to give the actual slope / gradient of a point on the graph.
Do you like my crazy mind?

• Chaminda Silva When both your points are the same, the secant BECOMES the tangent

• 7:47…Aha!

Didnโt I tell you guys she was a witch! ย ;o)

1. John Gray, CFA and Sally Miller are discussing what they think their year-end bonus will be and how they might spend them. Miller is new to working in finance and asks Gray what people usually get and what he has got in the past. Gray explains that the firm prohibits employees from discussing their exact bonus number but also says that 30% of people get โgoodโ bonusโ, 50% โaverageโ and 20% โlowโ. Gray says that he really wants a new smart watch recently released by a large tech company and says that he will definitely buy it if he gets a โgoodโ bonus, while there is only a 50% and 10% probability he will get it with an โaverageโ or โlowโ bonus respectively.

Two weeks later, Miller sees Gray in the office and asks him if he got a good bonus. Gray reminds Miller that the firmโs policy means he cannot say, but Miller notices that he is wearing the new smart watch they were talking about. Miller goes back to her desk and calculates the probability that Gray got a โgoodโ bonus is closest to:

A: 30%ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย

ย B: 53%

ย C: 57%

ย

Hint:

01010101 01110011 01101001 01101110 01100111 00100000 01000010 01100001 01111001 01100101 01110011 00100000 01000110 01101111 01110010 01101101 01110101 01101100 01100001 00111010 00100000 01010000
00101000 01000101 01110110 01100101 01101110 01110100 01111100 01001001 01101110 01100110 01101111 01110010 01101101 01100001 01110100 01101001 01101111 01101110 00101001 00100000 00111101 00100000 01010000 00101000 01000101 01110110 01100101 01101110 01110100 00101001 00100000 00101010 00100000 01010000 00101000 01001001 01101110 01100110 01101111 01110010 01101101 01100001 01110100 01101001 01101111 01101110 00100000 01111100 01000101 01110110 01100101 01101110 01110100 00101001 00100000 00101111 00100000 01010000 00101000 01001001 01101110 01100110 01101111 01110010 01101101 01100001 01110100 01101001 01101111 01101110 00101001 00001101 00001010

ย

PS: Nancy, if you solve this problem…Can I add you to my Christmas list?

• Dude how to solve it?

• “you don’t have to like math, but you can like my video”

• Welp, please upload videos on further trig…love u xx

• such a sweet voice

• Excellent explanation!

• what is the derivative of your number

• Obviously zero, bad question xD

• Lmao, it’s literally 0

• @Renovator i agree

• What I’m more interested in is the derivative of her number multiplied by x.

• Zero lol

• I’m an old man, but you are pretty, smart, adorable, and hot, anyhow, keep up the good work, your video’s are fantastic, and there’s no doubt they help lots and lots of students.

• Excellent video

• hahaha she got me when she said you dont have to like math but you can like my video *eyes to the camera. For that a like for you.

• Could you do a vid on integration by parts?

• Good job, NancyPi, the cutie pie.

• Thanks for the lessons that you’ve given me
The formulas are all in my mind
And now that we’ve come to the end of the semester
There’s something I must say out loud

You’re once
Twice
Three times a teacher
And I thank you

Yes, you’re once
Twice
Three times a teacher
And I thank you
I thank you

You shared my grades
My maxima
My minima
You made my undergrad worth living for
And if I had to repeat the semester over again, teacher
I’d spend each and every moment with your videos.

• u are amazinggggg!!!!!!! tnks Nancy

• thank you i understand it now.

• Youโre an amazing child of god โ๐๐

• Whoa, I like how the secant line moves with your hand. Cool editing!

• I love your videos!! They help me so much

• Great video, but I would have liked it more if you would have pointed out that the constants always cancel out in f(x+h) – f(x) and that we always need to pull out lim h->0 h/h = 1 as a term. I think these are important concepts, and they help keep the student on the right track while solving the equation.

• Definitely earned a subscribe!

• I hope you don’t mind me saying I think I love you

• Awesome mam๐๐

• Nancy you are a good teacher

• You’re awesome. Thank you so much–what my professor tried to teach in a week you managed to teach in 14:29 minutes.

• Nice

• omg so helpful, and the effects are just awesome! keep putting videos <3

• Find derivative of f ( x ) = x ^- 4/ 5? By definition.

• what an angel!! thank you so much for your math videos. im taking calculus for the first time in college and its been ROUGH…but these videos are helping me so lets hope I get a B on this exam wednesday! lol

• Perhaps it depends on having just watched other videos about this topic so, little by little, I had just assimilated the concepts but, apart from this, your explanation is the clearest ever ! Thank you again!

• Thank you!

• your beauty just makes every step you explain so easy. keep up the good work

• Amazing. At 5:18 you showed X in the denominator and it being cancelled out (leaving just h on the bottom). Until now, I’d never had it taught in those terms. Yours is a much better way of explaining derivatives, DQ, and slope. Thank you.

• Can you do a video on taking the derivative of exponential and logarithmic term?

• Thank you

• Nancy, your videos are amazing and they’ve helped me out so much! I was wondering if in the future if you could make your videos a little longer and cover more complex examples? Your videos help immensely cover the basics of a topic, but once it gets to harder problems in the same topic i’ll get completely lost. thank again for the great content!

• Great explanation. Also, I figured out how Nancy “writes backwards”. ๐

• Could you do a video about increased derivatives please?

• 7:48-7:58 what kind of witchcraft is this?

• Ever heard of video editing effects?

• I never watched that far, and started to read reviews.

• She’s obviously good with her hands. I can only imagine about the incredible handjobs she can perform

• I so wish I was the tangent line…

• She is writing normally over a glass wall. Thereโs a mic above her head, and a camera on the other side of the glass wall. @ 7:45, they use after effects (an adobe software) to make those movements.
Also, they mirror the recording while editing. She doesnโt write like that.
Youโre welcome

• just thank you …..

• Not only she can write backwards she has the ability to move lines and images with her thought. this is amazing. and speed up time.

• This was the best explanation I’ve found for derivatives. Thank you!

• derivative by definition of x^x?

• thank you , thank you , thank you , now i understand the derivative

• PLS do imagianryy zeroes ๐

• Need ASMR vid

• Let’s not kid ourselves. She’s gorgeous and smart.

• she really is

• @F.V. yours as well

• What makes you think any of us is kidding ourselves? It’s why all of us are watching.

• I love her!

• @Sapolsky uh no, just you bud. At most I will gaze, but i’m just here to learn. Her beauty and calm voice makes me more inclined to listen to her versus someone else.

• NancyPi… iam in slope with you!!!!!!!!!!!!:)greetings from Greece!!!

• Just reviewing for my final wishing I watched this when I was first learning this. But damn after we learned the power rule I felt like all this was pointless ๐คฃ.

• You are so much better than all my math teachers

• A most beautiful, illustrative definition of a derived tangent from a secant line. It is etched in my mind for eternity! THANK YOU.

• Yeah,life is not that simple…

• If a rope is drawn from the north pole of jupiter to ours and the line from our centre to jupiter’s is considered to be x axis and a watermelon is dropped from the top of the eiffel tower on an imaginary bullet train travelling under it at the speed of 0.001 mph …then, how many cookies has rosita eaten while watching the 6th episode of 3rd season of friends in the alternate universe where they actually are ENEMIES????

• Great Video! I would have won the noble price in physics or Math by now, If your videos were available when I was in school in 10th grade. Please do not stop. You are training a generation to like and do math. Thanks

• Mercy

• U have really covered everything I wanted to know well done and nicely explained…respect from an 8th grader of India

• you r grate

• How we ain’t sophisticated enough yet ๐คฏ

• you’re absolutely saving my calculus grade right now. the way you explain why the definition is what it is for each piece helps me a lot. thank you!

• Great job! Thanks!

• can you just teach the entire curriculum please

• can you please be my math teacher!!!!

• Thank you

• I missed the first two classes on derivatives and could not catch up…until NOW!
Thanks again for your dedication and selflessness.

• These effects are actually really cool, I wasnโt expecting this lol

• She explains everything so fluently and in a gorgeous way, uses some kind of magic with her board, she’s definitely a witch.

• What is this backwards-writing sorcery?!

• Hi i don understand

• wow smart and beautiful, either this is a artificial video or she won the life lottery.

• how can you say it’s okay not to like maths?๐ญ๐

• You are the best at clearly showing us how to approach calculus problems!

• You are awesome! I have been trying to understand this for at least 2 weeks now. My teacher doesn’t explain things as clearly as you do. Keep up the good work!

• HI Nancy, I recently discovered your channel after going back to school to finish an engineering degree….25 years later! I was never talented mathematically but I somehow managed to make it thru Calc 1,2,3 and differential equations before deciding I wanted to go in a different direction…..at least at the time. Thank you for the crash courses in calculus to get me back up to speed! Do you have any videos on differential equations? Thank you in advance!

• what is instantaneous rates of change.

• I Literally Hate Maths
But I love Watching Your Videos
And Seriously I Understand Every Concept

• Good job ‘ But can you translate into Arabic

• You are lovely!

• I hope you were my math teacher at school.

• Im so distracted ๐

• Is it as the x+h value approaches x value or the h distance approaches 0. Iโm confused. Please explain for me to understand. Thanks

• Your wonderful teaching abilities have changed math for me after many years of struggle. I can only thank you.

• This was extremely helpful. I introduced derivatives to my pre-calculus students and used this video to show the derivation of the limit definition of a derivative. This was also nice for showing the connection between simple slope and derivatives of non-linear functions.

• She could’ve used the power rule derivative instead of implementing limits in this example. nx^a to anx^(a-1)
n = coefficient
a = exponent
x = base
Multiplying the coefficient and exponent, then subtracting the exponent by 1
for example, 4x^3 + 5x^2 + 9x + 1
f'(x) = 12x^2 + 10x + 9

• This vid is about the definition of the Derivative; or in other words, the *first principles* of the Derivative. Power Rule, Product/Quotient Rule, Chain Rule, or something related are Derivative shortcuts, and in this vid, she is showing how to evaluate a Derivative of a function using first principles, NOT shortcuts. Moreover, if she used shortcuts, she wouldn’t be using first principles.

• U look so beautiful ๐๐น๐น

• Beautiful teacher ๐๐

• If only my teacher have had explained this topic as your have explained it. Thanks!

• Hi
i want to talk to you.
Wat’s app 8252319945

• Please a video on how your magical table and skill work! So genial!

• What if the graph changes drastically to where it has a different derivative at different points? How would you find the function and how would you know to find another derivative?

• If h is going to be 0 do we real even need to divide since In the end we will just be dividing by zero anyway?

• Jesus am I the only one watching because I love maths? So many creepers here.

• Your teaching style is put simply , “SUPERB”. Thanks for uploading.

• It wasn’t only definition but “Practical Deriving”.

• Wish I could write backwards that well.

• I really need these what is (topic) kinda of videos because it helps me to build the base of my understanding.Thank you nancy for explaining definition and i encourage you to do more for all.๐ค

• Hi thank you.. I finished my engineering school phase.. n I just understood this well about derivative

• You are so smart thank you for sharing your knowledge

• Cool

• Pliz am really confused at the point where the limit is approaching to zero do you mean that the tangent line at the specific point is zero pliz give brief explanation for me to understand guyz

• In other words h approaching to zero what does she mean

• Good explanation maam.

• 12:13 are u sure you can divide out the h from (2x +h) since itโs in parentheses

• she plugged 0 in for h… from the limit

• that moment when you have the looks and the brains

• thank you ๅค่ฐข

• Who came up with this stuff ? I mean I think I have no life, imagine just doing nothing one day and you are like “oh I think I am going to write this and than do this to that and maybe this too and it did not work so I will change this with that and that with this and ok it makes sense” seriously wtf ? Explanation is great Nancy , the best I came across but (f)-(d-d)uck my life.

• Lots and lots of different people and lots and lots of time, I don’t know about you but for me that really helps

• @james gornall sure it does, thanks

• Nancy looks like a prettier version of Alanis Morissette.

• She looks like Megan Fox.

• Am I the only one who thinks she’s so pretty?

• How does she do it??

• Whatโs the derivative of your curves?

• Math, Schmath. I just like looking at you.

• I donโt care about the math, but this beauty and sexy girl!

• Hi gorgeous!๐โค๐ฟ๐ ๐๐๐๐๐๐๐๐๐๐

• U respected must note down the deff ,prprpty,concept verbally i cannt get the point plzzz

• How u can explain the rate of change here is x not time im cnfused plzzz

• Nice work ๐๐๐๐

• Thanks, this helped me get a grasp on derivatives and their purpose since I wasn’t really sure on that

• pls do chemistry vids and physics

• Great video you made it very simple to understand, as a former math teacher I really appreciate this approach.

• I’m Nancy too, your tutorials are clear, easy to understand and amazing๐

• I appreciate the fact that you speed up the process of writing out the definition etc….

• Itโs very good illustration.. in simple way is multiplying that exponent to coefficient and just minus 1 from exponent..you end up with the answer 6x. The 12 will disappear because h approaching zero.

• Nancy Pi WELL. …

• SO MUCH

• NanciPi. More like QTPi.

• Geez Nancy, I’m sure you’ve forgotten more math than I will ever know!!! Impressive!

• Thank you for the video๐. I follow you from Morocco and I like your videos. I am very happy and wish you a successful journeyโโ

• Thank you Nancy. I am taking your videos as a reference each time when doing math with my daughters and they have both became good at it. The school marks are also confirming that. I appreciate your work and your commitment. Thank you.

• Gorgeous and smart.

• She’s hot.

• How do you write backwards?

• I came here for the thumbnail.

• i saw wide shoulders and i clicked.

• The tangent line slope is variable… That is all… /

• +1 Angelina Jolie teaches math.

• Nancy you are an excellent teacher, but why you dress like a “model”??
You are so attractive and can be a model as well.
But you can’t be both @ the same time, your male students will be failures! I wish this is not what you want ๐

• blackhole0608 She can wear whatever she wants. Her clothes are classy and her purpose and focus are absolutely on the math and not herself.

If you think sheโs a good teacher, then learn from her. Otherwise youโre just discouraging her to teach and screwing a lot of students out of good lessons.

• ayi yai yai.. megan fox lookalike… she should go for modeling, instead.

• sarvesh m Why? Then she couldnโt teach people. There are plenty of models in the world. There arenโt many good math teachers.

Sheโs here to teach math, not do a job you think is appropriate.

• @Andrew Wolff woah.. take it easy ..bro. are u her boyfriend or what? I’m just admiring her beauty; also i didn’t force anyone. Not many girls are beautiful and tall at the same time. She just can give it a try; may be she will earn a second income. Also ,she can do both; why are u pissed off? calm down and keep doing your math.

• sarvesh m Not pissed off. Other people in the comments simply said โbeautifulโ and left it at that. You literally said โinsteadโ so your second comment is just backpedaling.

I donโt know why I reacted. I guess I just see someone working hard and doing a legitimate video about math and because sheโs a woman, you focus on that. I guess, if I were her, Iโd just want people to take my math seriously.

Sorry to jump on your comment.

• Oh man. This brings back memories of calc class in college.

• Kids , calculus will make you smart and popular..

• 14 min to say nothing… but say it 30 times. ty for nothing

• God youโre pretty.

• Them some smokin’ curves !

• Good lord your parents have symmetry

• Thank you very much. Very clearly explained. Greets from Amsterdam , The Netherlands

• Mashallah

• Umhh yeah, like, duh!

• woah…the tangent line magic time warp…cool

• Thanks just remember I saw I understood I failed, I’ll be back. I also enjoyed your way of explaining with ART. I’m an Acadenic, Artist/Love Elon Musk too. I want to be a talent at Nuarulink

• Everything about her is impressive, right down to being able to draw and write backwards and mirror image. Wow! I wish I would have had Youtube 2 decades ago and access to this video when I was taking differential equations in college. I understand it better now than before!

• You’re hot. You don’t need to know all that science shit. You could just find yourself a man to take care of you. A man like me!

• Holy shit did you write that backwards? Mind blown.

• 2:27 “The tangent line is different everywhere”? I have 2 problems with that. 1) It is false, for the shape that you drew, there are several tangent “lines” that are exactly the same. 2) What you drew were line segments, not lines. Lines have infinite length and you didn’t draw those with arrows on the end so shame on you. 2 errors in the same statement.

• I find your methodology along with your voice mesmerizing. You are mesmerizing and thnak you.

• Hi Nancy,

Please excuse this question, but it’s not obvious to me.

1=0.999… Got it. I can appreciate the many arguments why this is so.

Conversely, why isn’t the limit as h -> 0 = 0? I’m sure there’s a reason why this is not so, just don’t know why it wouldn’t be?!

Thanks!

• Never thought Math could get me excited. Lol
You’re awesome at what you do.๐๐

• You got the slope of the seccant line!, nancy very good pi

• Beautiful and intelligent. What else could you wish for? I’ve fallen in love ๐

• limite when h trends to zero,nancy

• Thank you beautiful, you make calculus gorgeous and vice versa

• I love you. I mean, hi…..

• Beutiful and smart, Awsome !

• Excellent explanation! I wish you had been my high school calculus teacher!

• I would have gotten A+

• Obviously!

• My high school calculus teacher was like a 7 this girls like an 8.5

• Wow, how is she making this video.. we need a video on that

• All of a sudden Iove math.

• It’s great to see someone thinking through what they are explaining. The sign of a natural teacher.

• Nice voice

• are u standing behind a glass???

• the best way to learn advance mathematics. i wonder why i paid so close attention.

• the rate of falling in love with you is infinty.

keep it up please.

• So WHY would you want to know the slope of a curve at a particular point? Especially the kind of random curve used for examples?

• How to contact with you

• – Now, I get it! Which means that armed with this new information I can finally go down hill skiing, it’s all about the x,y slope. So when does the “z” enter the equation? Just incase I come up to a tree that’s in my way. That’s were Sony Bono messed up. Forgot about the z axis when calculating the derivative.

• This is what happens when smart people marry pretty people and have children rinse and repeat and then everyone is smart and pretty!

• Just wow.

• It’s not that pretty people can’t be smart, it’s just that they don’t have to smart to thrive in our society..

• She looks Stuck Up, but Smart

• Thank you Nancy for awesome explanation. What I got from your video is that the slope of tangent line changes along the curve and the rate of change of the curve/slope everywhere on the curve could be defined with an infinite number of these little slope values which themselves can be represented by a second function that tells you how the curvature of the line being evaluated is changing…..you made a subscriber out of me. Great job!

• I just want a sandwich!

• Your session are amazing Nancy #STRANGER

• Love the explanation I am following you I think.

• God, she’s gorgeous.

• Ever notice the faster you drive, the harder it rains?

The derivative can explain it.
But you know its wrong.
Because the rain didn’t change.
It only appears that way.

Must factor in relativity.

• It is good explanation, but there is something you used which needs clarification. at 11:59 you did fraction simplification for h: you assumed that :when h->0 limit (h/h) -> 1

• Excelente Nancy, eres muy buena.

• NancyPi is Very Hot.

• Excellent!

• Odd question but, is Nancy writing left handed and backwards so we can read it?

• no. these type of videos are filmed as she stands behind and writes normally on a clear piece of glass. the entire video is then mirrored so that we can read it.

• Sweet, less amazed -0.05%, but still impressed ๐

• ุญุณุงุจ ุงููุดุชู
..ูุดุชู ุงูุฏุงูุฉ ูุนุทููุง ุงูููู ููุทูุฉ ุงูููุงุณ ููููุญูู

• what was the 8th choice from the top in MS word font window

• I want to marry Nancy ๐

• just wow

• Wonderfully clear. I have not done math for decades and your explanation provided clarity like never before. I will have to re-view your video. However, I do not quite understand what a limit is or its purpose. Again, thank you again for being a wonderful instructor. You validated my suspicion. I always suspected that math could be taught better.

• Derivatives are all about rates of change. One thing is changing with respect to something else. Let’s say the economy is growing with time. You see on the news that it grew 1.2% in the last year. But then you read that it only grew 0.2% in the last quarter. And, in fact, it shrank by 0.1% in the last month. Clearly it grows at different rates over different time periods. If I’m interested in the current trajectory I might look at what it did in the last week, or the last day, or even the last second. (I know that’s kinda hard to do with the economy, but it’s just an example).

As my time interval gets shorter and shorter I get closer and closer to the _instantaneous_ rate of change, otherwise known as the derivative. You might argue that there’s no such thing as an instantaneous rate, but I will argue back that I can get arbitrarily close. That’s where limits come in. They let us talk about arbitrarily small things (or large things — but for differential calculus it’s always small things). Our notation for an arbitrarily small — or infinitesimal — quantity of time is dt. If E is the size of the economy then its derivative, or instantaneous rate of change with time, is dE/dt. It is “the limit” of the rate of change in the size of the economy as the time interval we are talking about gets arbitrarily close to zero.

What use is this, other than a fancy notation? Well, the world is about nothing if not change, and derivatives crop up literally everywhere in the physical sciences as well as economics and other social sciences. Using the technique that Nancy demo’ed, plus some handy shortcuts, we can deduce a lot of useful stuff.

(P.S. I went back to school after decades away from maths too, and got an advanced degree in astrophysics. Never too late).

• At 3:50 she says coordinant. That should be coordinate. Are we sure she knows her stuff or is acting, and actress?

• If math were really as boring as you make it out, we would’ve never made it to the moon

• Oh, actually, we never did – it was the hoax of all hoaxes. Oh, and your comment is bull on other levels too.

• Touchรฉ, darlin’

• Why she laugh when she is explaining? I don’t think the equations are funny…๐

• Because she kniws most of us are clueless….

• This maths crap gave me headaches at school later in life i now suffer migraines … go figure

• You are more lovely than derivative. Love you

• Great Video! Don’t forget! August 13th is National Left-hander’s Day! See you there!

• She’s writing with her right hand. The picture is flipped so that the writing is readable to the viewer.

• @dooovde hey…you’re ummm “right”

• you are fucking amazing thank you

• why r u laughing while explaining? lmao๐

• Because she knows most of us are Cluelesss….๐

• @Raul DยดEmpaire ๐๐๐๐

• This girl is a perfect 10.

• Ah but who won the rugby league challenge cup in 69 and 70 ???

• Mmmmm

• Great, im learning derivates and improving my english listening

• Nancy I would became your boyfriend

• She is actually righty . .in this video she is mirroring .. . Am I right ? ๐ค

• The substitution (x+h) to 3(x+h) ^2 is confusing.

• When it comes to plugging in values into a function, I find it best to think of it as like a “machine.” where any input of x that’s inserted into the function can be mechanically changed to give a new output value. The process is the same regardless of the value of x since f(x), the function, is defined in it’s relation to x.

ex: Find f(x) evaluated at x=2 where f(x)= 3(x^2) +12

(since the function can be evaluated at any point of x, we can just plug in our value of x which is 2 in this case and solve)

f(2)= 3(2^2) +12
= 3(4)+12
=12+12
=24

however when calculating the derivative she needs the same function evaluated at x+h this time (and we can do this because despite it looking weird, x+h is just another value of x, it’s just being added by some random constant h), like we did before for substituting 2 in place of x, we do the same but x+h for x now, thus:

f(x+h)=3((x+h)^2) +12

is the value of f(x+h)

when she was calculating the derivative through its definition of the limit, she just plugged in that very same definition of f(x+h) that was just found into the derivative formula where f(x+h) was. Since the value of f(x+h) was found to be 3((x+h)^2) +12, we would substitute this in place of f(x+h). This is also done the same for f(x) which we would substitute 3(x^2) +12 instead. Thus:

f ‘ (x) = lim f(x+h) – f(x) = lim {3((x+h)^2) +12} – {3(x^2) +12}
h->0 —————–
h->0 ———————————————-
h h

I bracketed the substituted terms trying to make it more clear. Anyways I think I’m done at this point but I do hope this helps you gain a better understanding of what was going on in the video ๐ .

Also @NancyPi awesome video, this was probably one of the best introductions to the derivative I’ve seen on YouTube!

• @Nucle4r Penguins Thanks very much!

• @ynotbegreat no problem

• “Only in one point” is not correct…

• Life is not that simple, i felt that

• YOUR AWESOME…I LOVE THE WAY U TEACH. THANK U

• So you are right handed then?

• The perfect woman doesnโt… ๐ฑ๐ฑ๐ฑ

• I have forgotten limits n function ๐คฆโโ๏ธ๐ฉ๐จ๐คฏbut seriously I’m going to catch up with that too..nice efforts n thx!

• You are better looking than my last math teacher.

• Awesome video! Thanks so much!

• What a voice! Soft spoken ladies like that… I could listen to you all day!

• …..wow Nancy idk how my gf is going to react after seeing this comment but trust me you are bae

• Nancy, are you writing backwards?

• GIRLS ARE NOT SUPPOSED TO LIKE MATH!!!

• curves

• and she also beautiful,,,

• I was a math major in college. My peers didn’t look like her! Gorgeous; smart; great teacher. Thanks for hitting me on all levels! โจ๐โจ

• At about 6:45 in the video, I don’t think you have a good approximation of the slope right at x. After all, we can see the slope is negative at that point. I know you’re getting to it though. As you move the points closer, the approximation gets better.

• Nice job on the explanation… I took calculus in high school but did not really get what was going on. The teacher started off teaching limits. I found a book in the library … Calculus for the Practical Worker … he explained it from a different point of view…this was an eye opener it was then that the limit method made sense to me

• so cute and lovely way of teaching

• Hi nancy. Are you single

• i don’t think so.she is not your dish.

• @wem wem who are you? Let her to answer me! I’ve been nice to her

• What is a “tangent” Mrs. Blue Eyes? We love watching you but not hearing you talk about mathematics — that is not your genre!

• In case, you didn’t notice, she was drawing and writing from right to left perfectly.

• yes, it is a skill

• Video is flipped….

• Probability of her being left handed is low too. Another math lesson for you

• You just made Newton and Welhim jalousie and made Cantor proud. You explained the limits in a nice talented way. A little production of Archimedes and infitesimal delma wouldโve been grate but I think you did a good job here .
Cheers,

• Nice mam

• she could teach me anything

• Ooo arvada bak

• Derivative was created by Wall Street Einsteins that caused the 2008 crash so my dear you’re a little late to educate us on derivatives.

• Have some respect . She’s an MIT graduate . MIT graduates do MATH at a very high level so they can be prepared to be scientists in the best research and development labs anywhere in the world . She took courses and passed exams which are serious . Instead of being jealous of her you should take her as an inspiration for you to be like her and do more and better for yourself and for the world .

• I love calculus…now.

• Your facial expressions make me feel like you yourself are not fully convinced๐ฌ

• This was a great way to explain the concept although I think you made a very minor mistake somewhere at the end of the video when you said that 6x is the derivative of the f(x) at “any” instant. Does the slope of the tangent line not change at different points on the graph? Nonetheless, beautiful explanation. Thank you, Nancy!

• Yes it does change, and so does 6x for different values of x. She did not make any errors. By any instant she means any x.

• @Marco Pisano My mistake. I apologize.

• we should do some math sometime! maybe you can teach a really dumb model how to solve fermat’s last theorem …. ๐

• I have to do this the next year… jeez!

• You explained rightly

• What is this lady’s background?. Anyone can post anything on YouTube these days๐คจ

• She’s an MIT graduate . It’s in the video description . MIT stands for Massachusetts Institute of Technology . The MIT is the nยฐ2 University in the world for 14 years in a row in the Shanghai ranking .

• @Farouk Abdallah Dude, I know what MIT is. She’s the one who’s completely unknown.

• @rthelionheart So at first place you doubted the lady’s competences by asking her background , and now knowing her backround and understanding that she has competence you say she is unknown … What being known or not has to do with practicing math ? Being from MIT isn’t enough ? And there are 25 000 students at MIT , could you know all of them or even 10 of them out of the 25 000 ?

• I only have ADD with this teacher

• Hey Whitney Cummings is a math teacher!!

• women what?

• Very Helpful in understanding derivatives, Please also make a video explaining basic integration.Thanks

• loving
me from Pakistan

• yeah…so what was I watching?

• Thank you mem… God bless you

• I first took Calculus 50 years ago. Thank you for the clear and concise explanation of what the derivative is.

• Youtube hate science this is the fourth channel of science from which I am unsubscribed for no reason I just found another one now about 2 hours, 2 hours and a half so if anyone of you has this shit problem with Youtube like me that is no coincidence. It’s direct sabotage from Youtube itself

• Very great

• Oh hi, excuse me… What are you doing going?

• Very nice

• She Writes Backwards Most Beautifully

• she does not write backwards

• Yes She Does She is Writing Backwards so the Audience Can Read it Forwards

• @Mark Hammarskjรถld NO, she is behind glass and she writes from right to left and we see it written from left to right

• If You Were to Stand Behind Her You Would See She is Writing Backwards… or She is Writing Forward and Then Flipping the Actual Video To a Mirror Image or Flip Horizontally in a Video Editor…So

• she is so fukin clever

• thank you Nancy for helping me get thru Calculus and Econ 2

• Resolution is the question. it is impossible to calculate as it divides infinitely which is why we end up using constants, so it will always be an estimate.but then again, what the hell do I know., i’m just a mechanic ๐

• 7:48 WITCH WITCH SORCERYYY

• Math became so beautiful…

• “Greater than Zero but not Greater than the function x; f(x)”

• Nice

• Great trick to sell your beauty.

• tight โฆ..

• Plot twist: the video is actually played in reverse

• I want to know how you make this type of video…. it’s written from back side…plz tell me how?๐โบ๏ธ

• Video editing software!

• nanacy you r very beautiful love u

• Omg… I understood all… Tqqq โคโคโค

• Hii..
U r so beautiful…

• I wish you a beautiful career and life! You seem to have all variables under control.๐

• Such a beautiful teacher all will love maths

• She is not writing backwards, the image is reversed.

• I think this should be a test for stupidity or possible naivety given from the very start these videos were being posted you get morons asking can she write backwards. What a stupid question to ask lol.

• No man it is mirrored

• @Zhiguo Wang my old orthopedic surgeon had those in the exam rooms at the hospital she works at. they have them to make it special for the kids

• @Zhiguo Wang Not *that* complicated: it’s a glass chalkboard pumped full of light. Bright light-emitting diode (LED) lights are placed along the bottom and top of the glass and reflect light within the glass pane. When you draw upon the Lightboard with a coloured dry erase marker the LED lighting causes the marker ink to glow. Multiple coloured markers can be used for further impact. More info:

• Look at the large number of upvotes the OP got, compared to the meager upvotes the the sarcastic buffoons got. It was useful info.

• Our teachers were speaking different language when they taught us. They made sure for us to feel stupid.๐๐๐๐

• Wow she is so sexy ๐๐
From which country does she belong ?

• China

• So beautiful teacher ๐๐

• math coupled with beautiful eyes

• you are so Beautiful

• I’m from morocco

• How u do this type of video can you plz explain

• Google ‘light board’ or there is a video on you tube explaining it as well

• Really helpful thanks you very calm when explaining makes it easy to followโบ

• who is watching her instead of learning? in fact, i dont need to learn this

• Me๐๐

• thank you for taking your time to share your also for teaching much love and respect

• yep, not a clue about what you’re talking about, this is so difficult.

• What do you eat?

• WHAT????

• ๅธฅ้ฟ

• Fascinating. I wish I could really get this

• I followed you until you wrote that formula near the end. I solved it at the end, but that’s too much math for the year. ๐ฅด

• Awesome work! Explained much better than the way my teachers did in both HS and college

• Wait what!! Is she maths teacher ๐ฑ ๐๐ if I had teacher like you I would have topped every maths exam…. You are hell gorgeous ๐๐๐

• Thanks mam……love from India

• in love with maths from now onwards

• Girl, you make everything so much easier!!!! Thanks – alot

• clap for him

• ๐๐

• Clap๐๐๐

• ๐๐ป๐๐ป๐๐ป

• Hi Nanci, It’s a great video and your way of explaining it is really helpful to many. I would like to request you to post sequel videos for Calculus and Linear algebra if it’s indeed possible.

• Boa aula de derivadas ( Derivative)

• If my math teacher was as good looking as you I would have 2 PHDs In math and physics

• Youโre the goat

• who cares anymore? world is going to crash! you people have no responsibilty for africa, the poors, the weak of this planet. so why care anymore about your sayings? WORLD IS IN A VERY FAST CHANGE THAT WILL STOP ALL YOUR EGOISTIC WORKS!!!!!!!!

• Humor you? I would worship you. All my math teachers were grumpy, grizzled old guys with bad breath. This is sooo much better!

• Nancy i can prove pi is 3 , looks like your a Pi fan

• thanks soooo much for this explanation! it’s really easy to understand.

• I LOVE YOU

• Thanks! Helped me out a lot!

• Finally! The clear, half graphical, half algebraic explaination I was looking for. Thanks for the clarity and the consistency!

• Nice to see a smart, non-tattooed, non-blue haired, non-obese woman teaching math. A rarity in society today.

• Fantastic math class. Very good explanation.

• Thank God for suggest your channel

• You are so gorgeous ๐๐ also best teacher, thanks alot๐๐

• WOW

• Let’s be honest – Nobody came here for the math.

• Why did u come here?

• @Sania 0.0 It’s a joke among the thousands of this type.

• @Djentstructer 5000 oh ๐๐๐๐๐

• They say that gamer girls are awesome but i say that a girl that loves math is better

• I am a EE and I am getting a MS in EE. I did a bunch of mathematics. I have to say you are doing very good. Very good explanation. Do not stop. Thank you.

And before I go can you also do some Caley-Hamilton theorem , Jordan method , some Eigen values and Eigen vectors video.

• Amazing!!

• Dear o dear, derivatives??? No, there is nothing on this subject on YouTube. Pfffffff, another useless video.

• Just because you have no brain, it does not mean it is useless.

• @freak777power Try to read, my dear! She’s doing something that has been done over a 1000 times before on YouTube! If you want to see beautiful/sexy women go to another site, please. Her presence in this video is totally superfluous!

• @Veronica Noordzee your vocabulary is to sophisticated for me!

• @Justin Y 2.0 I can see that, haha. Next time write “too sophisticated”, please.

• @Justin Y 2.0 You meant to say, your vocabulary is TOO sophisticated for me. Yes, I now can understand very well ๐

• Without her I would have failed my precalc class and I would be failing my calc class now,Nancy you make girls like me love math as a skill rather than an obstacle to overcome

• im not into derivatives but wide shoulders

• Ive never seen such a good looking smart person. She is incredible.

• Thank you Nancy. Literally, I’ve been to tutoring, watched Chegg videos, other YouTube math videos, but yours is by far the most explanatory and I really get you. I like the fact that you dont try to make it hard and confusing as well as being open to new methods and easier ways for different learners. You amazing and beautiful too ๐

• i dont care about math.. i just came here for those eyes

• Super……. ๐ฑ

• For the first time in my life I know what derivative actually means…. Great Job๐๐

• @Danny Co A message to me that begins with a snarky insult doesn’t deserve a reply.

• @Danny Co Not at all. I can mute you with a click of the mouse. Bye.

• A derivative is the same as a slope of a non linear function.

When I was a Business student at Saint Mary’s University during the 1990s, I took an “Introduction to Quantitative Methods for Commerce II” course, which consisted mainly of Differential Calculus, Statistics, Sets, and Probabilities.

I also had to master the four different derivative rules, Power, Chain, Product, and Quotient.

However, we didn’t learn about anti-derivatives or Integral Calculus, but its easy to master once you learn the fundamentals.

• @Ruthless Goat are you ok?

• @TXU bby I’m fine. I guess the jerk in question deleted his messages.

• Can I get “h” in my final answer?

• NancyPi mmhmm

• wow thank u

• u made me understand maths so easily cuz i m the girl who used to score bad at uni exams….one more thing….u can try for miss universe ๐ cuz u r sooo beautiful …i wish i had yo beauty :/

• I love Nancy Pi, I have an A in calculus and I understand it, thank you miss lady!

• secant line doesn’t ‘becomes’ the tangent line. stop saying that.

• Nice

• It was likewise explained to us, except that he was an elderly man. Well, neither am I the youngest now. ๐

• May I have your email?

• Great effect on the pink line at 8:00

• Thanks mam. I Also undertood well.

• I canโt focus on what she is explaining.

• ( . )( . )

• If you can pull your head out of baphomet’s arse, you might.

• Try harder !

• Why does Homo Sapiens deal is with itโs consciousness of sexuality so hypocritically?

• you are not alone …

• (3x^2 + 12)’ = (3x^2)’ + (12)’ = 6x
(3x^2)’ = (3)’ x^2 + 3(x^2)’ = 0 + 3 * 2x = 6x
(12)’ = 0

• This is the best “low down” I have come across! your awesome Nancy! thanks for doing these!

• Iโd like to go low down if you know what I mean….

• I love you! Beautiful and smart. Btw joke aside, it was wonderful lecture. God bless you
Peace out!

• very nice. plz do one on integration by parts

• Nancy, I studied up to the derivatve wout a shhool or teacher back in 1964. I don’t want to horrify you. The truth is Virginia had framed me for first degree murder in 1960. I found books on algebra I and II plane geometry, trigonometry, and calculus. After studying math every day after outside field labor and on weekenda and holidays, I got to calculus. I learned how to do the derivative using the deltas. Then I saw the short form or the power rule. I had a book on old school college algebra. So, I saw the powerrule quickly. I had twenty- five years. In short, I did not make paroll until 1974. A move came out with the title “Welcome Home Brother Charles”. To learn more about what I passed through in prison, just Google Charles M. Abernathy v. W. K. Cunningham. I went to college after leaving prison. However, I majored in mass communications/journalism. My minor was mathematics. Now, you are helping and inspiring me to finish my math studies. Thanks, Nancy and all of the YouTube math instructors. I love mathematics.

• This is when you cant hide your american accent

• I am proud to be a member of the human race just like her. NOT. She is so perfect it is ok for a grown man to cry in his pillow over her…every night.

• Damn, I wish I had had a math teacher like you when I was taking Calculus. I’d have been the most motivated kid in the class.
Anyway, the way you give the definition of a derivative is exactly the way our textbook and professor explained it but they added a couple of things. He said the derivative had three basic interpretations that were all correct. First, the derivative is algebraically the limit of a difference-quotient. Second, the derivative is geometrically the slope of a tangent-line. And third, physically the derivative is the rate-of-change of one variable with respect to another. I think you alluded to all three but didn’t spell them out.
Subscribed.

• Wow! A beautiful young lady who can explain calculus so clearly! Nicely done!

• ๐ฅฐ

• Wow! I think you finally made all the pieces click. Thanks.

• I really focus on your eyes only. not in what you are teaching me ๐
.. so gorgeous and smart ๐

• tomorrow is our exam on calculus cant even focus what shes saying coz shes gorg as fck HAHAHAHAAHHAA

• I was wondering how they made super rollercoasters safe, now I see the applications. Thank you.

• I dont know why I subscribe here, but shes just like a magnet to me.
I love mathermatics but since i had some brain hemorrage or something, i had a hard time remembering things.
But I really do love mathematics and would like to get back at it some day.

Now just using the math in Stock Trading, fun and easy…

• it is not important that you teach me.but it is important i appreciate your beauty. good looking.

• These videos are great. I can actually understand them. My professor can get really deep into theory and misses a lot of basic explanations, but I’m getting it all here now. Thank you!

• Is NancyPi left-handed or right-handed? This is the key to understand how they prepare a video like this. Well, the answer is that she is right-handed, even though, she seems left-handed in this video.

• Plot Twist: She’s right handed.

• I am right handed and i can write backwards with my left easily

• This is all covered in the standard Calculus texts, at least the ones I was familiar with when I was an undergraduate. I guess if one is averse to reading then video instruction is a necessary substitute.

• Wow wonderful

• U r v cute mam

• Given that the x is always = y + h or in this case it’s just x, and in this case also the x + h is the sum of the two values, and when the h is the same as h especially, then the double of the y = the double of the x and then the slope becomes a mere function of the doubling of the sum of the substituted values, in this case easy to determine, but if not you just add another variable and then double it to divide it by the function of the simpler value, or z. Thus you get it.

• I must say that she is brilliant teacher.salute

• ๐๐๐

• She is burning hot๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ๐ฅ

• ๐ How can one get it between the babe and figuring out the magical backwards writing in the air and the graphics animation. ๐

• I actually thought the video was super clear (assuming you’re kidding of course). But I also found the speeding up and the whoosh of the breeze really funny.

• Writing backward is very creative but writing on a board would be much easier to fallow. It is very distracting to write on glass.

• This is a particular case in a single variable. You need linear transformations for a generalization.

• first line derivetive is a slop at a point on a curv not a rate , rate is when somthing diffrnsiate w.r.t time

• It’s all about calculus until calculus has cheekbones.

• f Derivatives what’s up girl? ๐

• Get a personality coach.

• I pressed the Thumb-up button after First Millisecond of this video!:).. and subscribed after two milliseconds

• i want to be your derivative so that i can lie tangent to your curves

• simp

• Haha. Genius.

• When you aim to be a lover but end up loving maths๐

• Evil genius ๐

• I am waiting for your answer

• Thank u so much!โค๏ธ

• thought you were going to talk about finances.. ๐

• This is a great video, very clearly explained!

• I just subscribed. Not necessarily because I want to learn.

• I’m here purely for the calculus.

#NoThirst

• Hi Nancy

• ah yes my daily asmr

• The average adult male seems preoccupied with
Mammalian sexuality, not Mathematics!

• Alright Rob go do boomer things

• Nancy. U R a genius. keep that way!!

• Ahhhh..SecC

• That girl is fine! I wouldnโt mind making a couple of derivatives with her.

• You speak at a pace I can fully understand. Thank you!

• I want to be your sweet dady .

• i ate my crayon ๐

• Be a teacher in mechanical engineering class. Please

• If she is our Calculus teacher, Iโm sure weโre all gonna just gonna wack-off in class.

• Gorgeous and smart teacher. *subscribes*
The explanation of derivatives was so clear and well animated!

• unfortunately she sounds like miss south carolina … such as the Iraq.

• Simplemente HERMOSA

• That was incredibly helpful, I just had my first lectures on derivatives a couple days ago, and this part was breezed over as if it were assumed knowledge. Thank you for breaking it down.

• Oh my lawd… Iโm filled with Calculust…

Mean Girls on Broadway reference.

• I don’t know much about math but I can count to 10 and she is a 10

• You probably worked really hard to make this video and that is great but I really couldnt understand what you were trying to say It felt like you were repeating yourself a lot and try to justify the reason to learn the stuff you try to teach, I think that you like math maybe “love” it but I feel like you are trying to be someone who pleases “everyone” and doesnt please herself. (purely my opinion but you should try to du stuff how you want to do them)

• Who cares. How you doin?

• Best channel on youtube….

• The question: What is ddddtiv? My God, what a high speed! My gosh.

• Omg LOVE YOU !!!!!!! โคโคโคโคโคโค love you ๐๐๐๐๐๐๐๐๐๐๐

• very good thank you

• Math is hot

• Cute Nancy, come visit Uk… x

• I think it would be important to point out the danger of h actually becoming zero which must not be allowed to happen. Approaching or tending toward zero allows a mathematically rigorous result in that magical moment where h finally disappears and the slope clicks into place as the final act in an inching closer and closer process. This is mathematically beautiful. As for Nancy’s mirror writing – if that was live it was amazing but I am suspicious . . .

• The basic intuition is: the tangent of the angle of a pythagorean triangle of “infinitesimal” size (e.g. arbitrarily small but never zero). As this notion is problematic in itself (how small?), math people created the theory of limits, to put the foundations of mathematics on “solid grounds”. Doesn’t matter if MIT or any other school, this is the sort of “this shit works so take for granted and forget your philosophical misgivings” until you study real analysis.

• I guess this derivative is not about financial markets .. ?

• Seems strange the way you are writing. looks like you are writing on glass, are you writing backwards so we can read left to right? If so, I am impressed! ๐

• I flipped out when i was younger and realized that this woman is not only great at math but sheโs writing left handed and sheโs writing everything backwards. Like how ? And all at the same time?

• serious?

• I am an electrical engineer, I do research on electromagnetic field with simulation tools, I am very good at advanced calculus. I know Riemmanian geometry and topology. And I am watching this video. I just want to know what the derivative is, I guess…๐๐

• A man of culture, that’s who you are.

• it was pity that I was never teaching math with teacher like You…You know what i mean:)

• This really helped me! ๐ Thanks so much! Youโre a great and beautiful teacher!

• cutest mathematician in the room.

• I ever like direct instead of beat up @ da bush ๐๐๐๐

• Can we just clone her ?

• Dammmmn , Iโm in love with this girl ๐๐

• hi nancy

• This was very pleasant to watch, and the explanation was great.

• So enjoyable to learn maths from a smart woman on youtube. I must nevertheless confess that it takes all my will power to focus on the explanations and not let my mind be distracted by the charm and sweetness of the teacher. :0) Good job Nancy!

• Si en el secundario hubiese tenido una profe asรญ, en lugar de la bruja que tuve, habria aprendido bien las derivadas !!!!! Saludos .

• I just clicked to watch.

• Am guessing she has 2 degree, s in maths and physics

• I never had a math teacher this pretty.

• damn..she is sexy

• Can you also do a linear algebra course??

• Why did you choose maths for bf

• Of something idk

• she writes backwards in the mirror image with the left hand?

• Plz make a vdo on Maxima-Minima

• Take it I’m the only one here that doesn’t know wtf she talking boutcuz I’m confused

• ใใใใใใใใฉไธ่ง้ขๆฐ๏ผ
ใชใใงใใใใใซๅบใฆใใใใ ๏ผ๏ผ

• I watched the whole video avidly but learned nothing. I wonder why..

• She is great and one would hope that we would have a better math to calculate this.
It looks like a wave so maybe some kind of wave function or equation would make it easier? Watching this math is like pulling teeth orย trying to describe fractals without fractal math…

• Just watching this vid because of her i donโt even need to know any of this

• my teacher tell me to put the lim in the end of simplifying. if i do like you did. is it right???

• You are so beautiful ๐

• Wait a minute. You are beautiful and you’re smart. Why the hell aren’t you fat?

• My …..

• I m in 7 th class why i am here

• please make a video for complex number

• I am currently studying machine learning however I never went to college so my primary source of study is basically Youtube lol. Anywho, I found this to be extremely helpful in understanding the back propagation algorithms in a neural network! I look forward to more of your videos as my learning progresses! ๐

• So awesome, thanks so much!!

• Mam please little bit speed up your voice

• Slope witchery!

• I wish that you were my teacher in the University rather than the loser teacher in KFUPM

• She doesn’t write backwards she reverses the video of her writing forwards, you can see where the video skips just before. Call off the witch hunt.

• Great writing honey

• Shes hot, smarts has a nice voice and can write backward. Sheโs perfect.

• The image is reversed. Fortunately, I’m guessing the ability to write backwards is not really on your list of what makes a woman perfect.

• Do you honestly believe she can write backward, you get tricked easily lol. I mean there isn’t a human on the planet that writes english and maths backwards so I don’t get why you think its some special trait a person can learn.

• eystle girl

• @Ghost572 I can, it’s not too hard.
Try it yourselves

• Hi,I am interested to create and publish my math video lectures on your YouTube channel

• Mam can u plz tell me where is your institute… I’m very poor in maths. .๐ฅ๐ฅ

• I didn’t get this in 1990, still don’t.

• my gf wants me to watch a different math youtube channel bc this one makes her jealous.

• Walk away now!!

• yjreayudiyf

• ๐!!!

• lol Just put on a monocle when you watch and say things like “Indubitably so.” When your gf sees how serious you are about the math she won’t be jealous anymore.

• @bors b ๐ญ๐ญ

• All I can say is wow !๐ง

• I already know what derivative is but I’m still gonna watch it, who cares! Right?

• Because of the tutor isnt?

• @Julita Aishah Nah, is good to review this kind of things. And the tutor explains really well

• @Axl Rose you guy just want to watch it because of the tutor is pretty. What if fat black girl be a tutor..would you watch it? Admit it babe!

• @Julita Aishah I mean, if you see that a math video has more than 300k views and 90% of the thumbs are thumbs up, you can deduce the tutor explains things well. I would still watch it if I’m interested in the subject(like in this case). Sorry but you’ve lost this one, you girl

• @Axl Rose ouuh whatever..im not talking to you man!! Im just write it randomly.

• Hi,thanx,if nonfrinitum)function)^0=1,but nonfrinitum function non caunstant thus 1 be a function darivtumIntegrum of peristalsum of non linear (noninfrinitum)function INTEGRUM to ST/G FIELD OCEAN,love,bliss thanx XAMichael XAMBUNJILOM

• or get a calculator

• She maybe good at math but she canโt spell โsecondโ ๐ secant!

• Cali campeรณn !

• Notice that she is writing from right to left but we are watching her writing normaly from left to right .shit .

• wow this is the best and most thorough explanation of a derivative I have ever seen. Thanks Nancy for taking the time to explain everything.

• i don’t understand a word, but for some reasons i love to watch this vidรฉo.

• Intelligent and a beauty….. where is the hook? (Translatet from german๐)

• I guess she is a twin sister of Megan fox.

• So does she write all this in front of her and then mirror the image before posting?

• Thanks for the good explanation , keep up the good work. greeting from Arabia.

• Thank you.
Excelente video.

• Thank you, Nancy

• It has nothing to do with this videoโs contents, she teaches very well.

• Pretty good video, exquisitely edited, produced and double purposed. You can either learn calculus or delight your view with a beautiful highly educated lady.
Of course it deserves a like.

• Wow, first time I find derivatives could be so interesting (i.e. I was watching for more than 10 seconds… I could listen whole class). Derivative that! ๐ (I bet her students must be quite good at it)

• Sexiest teacher on planet ๐คน

• THANK U
โค๏ธโค๏ธโค๏ธ

• muy bien explicado, gracias desde Madrid. well explained, thanks from Madrid. ยฟEscribes como Leonardo? Do you write like Leonardo??

• I missed everything that she said.

• Nancipi stop everything you do in life… we know you canโt actually write backwards you flipped the screen we tried it to see if we were correct and we were write I liked youโre vids now Iโm a hater

• Really helpful for me

• kids IQ will tend to infinity if Nancy became the derivatives teacher while lim h->0 :), i have no idea what to tend to ๐

• Ppl say math is confusing, what’s confusing is I actually got this. Thank you Nancy ๐

• Yo ni siquiera se Ingles…

• Beauty and brains were very well. Thanks for been a good presenter

• Mire ha mi yo tengo halgo ke exponer sobre Hoyente ha distansia local y mucha cosa pero cuando duerme el fuersa de comunicasion adisional de generasion continuada hasta dias de hoy tanbien cuantas persona aplicar esa MATEMATICAS no entendible o con un ofisina de ufolojia se puede denunsiar el primer caso

• Mam please make the video of statistics of class 11 .

• Grow up, dweebs.

• This video was recommended to me…. and although I’m no longer in my calculus II course, I become a bit nostalgic of the times I would stay up late watching your videos to solve just a few questions… ah good times! Thanks for your help during many countless efforts at my homework and exam preps!

• Are u sure ur a math teacher

• Me too. Shes talking alot about x. Like how many 6 x she had in one derivatives?..

• When a beauty girl taking something incomprehensible to me.

• Nancy your way of teaching is excellent.

• She is so pretty for math

• She’s the dream math teacher

• she mirror-writes like Leonardo.

• Smart and sexy.. Most wanted wife

• I got a PhD in Physics, a major in Physics and two minors, one in Computer Science and one in Pedagogy. All of my professors were ugly and bad looking. If I had met you, I would have fallen in love from the first day, and my life would have been different… Who cares about derivatives, after all?

Anyway, nice explanation (and charming voice tone)!

• And you would not have had any degree since you would have been too concentrated on something else…hahaha

• Holy shit dude you have some serious academic accomplishments. Good for you and way to go. Impressive.

• THE ANSWER IS CALCULUS CHEEEF

• You should turn comments off on all of your videos. Too many disgusting men comment here. I am not male, my YouTube handle is pseudonym.

• Thank you so much for this explanation. You have no idea how much this bothered me. I’ve been studying mechanical engineering for over 5 years and just used the derivative rules without knowing what exactly I’m doing. So this helped out a lot.

• ok this is all very nice but…
how do you do that mirror effect on this video !!!!

• I hate to correct a girl that I have an insti-crush on, but you’re pronouncing “coordinate” with an extra ‘n’ at the end; i.e. the last syllable is pronounced “nit,” not “nint.”

• CuteyPi

• Hey @nancypi ..i study less n i only watch you…u so beautiful

• Great explanation thanks tho.

• Why we take Y as f (x) please Nenci tell me

• thanks teacher i got 75/100 in my cal 1 test thanks a lot

• She’s gorgeous, I can’t focus on the explanation.

• telllll me about it hahah

• hahaha lol

• may I be your Fourier transform ?

• Could you explain fractional derivatives ? (you are fckin hot!)

• Trust me , no one came here to learn derivatives .

• I miss your channel

• Subscribe for beauty with brain

• HOW NANY HOW?????
HISHAM ALSO WANT U

• You can do mathematics with me all day longโค๐๐

• Nancy stop the maths lets get to chemistry

• NancyPi, it makes my wavy Ocean Liners ๐ ( Derivatives )

• where do have your board? thank u so much

• Thank you

• it is not posible to focus…

• I came here to learn derivatives.

• So you are saying that the point where her hair touches her shoulder has a slope, and we can touch that slope if we try to think about it, using calculus.

• I did not understand anything.

• If ur my teacher I will never skip the class lol just kidding

• Like it you put it out simply .who needs school when we have this channel. Years later all this made perfect sense with calculating constructions fem method , although now software does it for you but basic understanding is extremely important.

• Where is the f(z) ..speed equation..beside the โslopeโ..#xyz3dtrading

• Half way through the video Iโm like ๐ณ๐๐ปโโ๏ธ but I love slopes now โฅ๏ธ๐๐๐ป

• 15 points๐ญ๐ญ๐ญ๐ญ I wish if I watched this video before taking my exams

• how does she write backwards ?

• Teaching math in TROPICAL climate…

• Excelent.

• Did you really wrote that in inverted form? You alien.

• My attendance would be 100% if i had her in my college life..

• If we have a teacher like you at the Uni, I will attend all my lectures at my uni everyday, even if it’s off I will go to the Uni. I wish I were a mirror so you can write on me.

• I’m not interested in a thing like Derivatives … but watched the whole video. ๐

• Mathematics is really beautiful ๐

• Why am I even here? She’s talking Chinese..

• FEEEL GIRL FEEL

• yiure not beauty btw,,,very bored,,,,its easy….,,,,

• Wow that’s awesome I’ve never heard it explained like that. If my T.A. in college would have explained it like you, I might have been able to actually understand it. Thank you.

• Finally. the best explanation ever. I get it!!!

• I suck at Maths. Good to know!!

• Well, I did take Math at uni 2 decades ago – now have to help my middle school daughter with hers, and needed to ‘refresh’ (first understatement of the new year) my memory. Turns out these videos are all I need. In fact, I think she would probably do better by directly watching this, than me explaining it hah ! But I’m going to watch these anyway.

• The fact that this girl is so smart and intelligent makes her even more beautiful. Like all class. What a catch total wife material all day..

• In all seriousness though, thanks for this nice instruction and explanation. I’ve watched a few of your videos as I have been doing a lot of upgrading. All the way back to logarithms Haha.
HAPPY NEW YEAR

• Great combination beauty + intelligent. They never come together but this one breaks the rules ๐

• this is great help Nancy and gosh you are beautiful

• This girl is so HOOOTTT

• ๐

• Nancy do you have lessons on Tensor Calculus and Vector Calculus, I think you might be my only hope of learning those.

• I love how personal this is. I love the way you move the secant line with your hand (Should have attached the dot to the line and moved them together, maybe). The acceleration noise is perfect.

Simple, novel, brilliant; Subscribed.

Keep up the great work. Really. Keep it up.

• She’s HOT ..

• 0:21 Yea yea show to me๐

• Sexy calculus

• Hmm, yes I do math.

• I knew it before but I think now I know it really better. Great Explanation.Thanks.

• I am not misogynistic, but I would never bet that she would know math =))

• I forgot derivatives after watching this video

• I am from Pakistan,you are speaking a bit faster,I mean it is a bit difficult to understand your language,so if you๐

• nancy pi & hannah frrrry — yeeeeaaauh

• How you edit the video ๐๐๐

• Thank you. Made that more clear than any math textbook. Also, you didn’t say it is up to us to take initiative. You taught.

• Nancy is to math what Nigella is to cooking..

• 11.57-12.00 “Now we can just do some algebra!” …( proceeds to race through 5 complex limit formulae and solve for the derivative.)……….I think I’m in love!!

• I love u

• A Scottish mathmatician created derivatives but this guy liked whiskey a bit too much…

• Thank you so much for your very informative videos! I like how you explain the concepts in simpler English than my textbook. I also like how you use the clear board!

• Thanks mam it’s really helpful

• Advice request: I have a nephew who just completed introductory algebra, and I want to give him a short introduction to calculus and why calculus is important. He hasnโt gotten to slopes yet, and he may or may not have gotten to exponents.

Can anyone recommend a good resource or, if youโre up for a challenge, a nice summary of what calculus is and why it matters? I have been pondering this for a LONG time and I never thought to ask for help (oops!).

Why do I care? Because a LONG time ago, I asked my bitter but brainy older sister the question โWhat is calculus?โ and her annoyed reply was โItโs about finding the volume of an irregular object.โ Yes, thatโs one application, but it didnโt answer my question. My goal is to do better than my sister did in giving a brief explanation of what calculus is.

Any help is REALLY appreciated!

• If F of X is Y, then can it be said that the F of X is also Z, or the F of Y is X, and so on?

• Basically, it is a scam

• Hi Nancy, you are awesome.

• Most of you have been bewitched! This is not a woman you’re seeing, but a man! Those of you who have taken anatomy and physiology will be be able to notice the masculine features on this person.

• The only part I didnโt understand was how you moved that line back and forth between secant and tangent. Are you a wizard?

• Big question does she see everything’s mirror image ?

• If I taught you guys the derivative of a function, you would quickly shut me down, leave no comments and watch some random youtube video instead. Nancy I hate you…J/K๐

• Step by step instruction by Nancy. {drools}

• that was fucking great

• Beauty with brains!

• Amazing definition

• Amazing she’s actually really nice and genuine in her explanations and subtly explains the concepts like you are a dumbass, although she’s so nice about it, that you don’t even know how dumb you were until after she’s explained it. All teachers should teach this way. So many of them either explain things the “smart” way, or they get annoyed when you ask them about a small detail that they, but not you, find irrelevant or obvious.

• Nancy, these are great explanations of maths. I am learning something. Thanks.

• It was 5 AM when i watched this. Funny how you grabbed me and makes me stay here for 14′. Well played it’s very interesting !

• I know derivatives but don’t know how to use them in real life ๐ท

• Love ur teaching skills ๐คnd love you too ๐๐

• God bless, you are saving my finals

• The smoothest operator of educating mass scholars in derivative functions for the slope tangent of a curve… “You don’t have to like math; but you can like my video”.

• She is merely average in Mathematics.

• Honestly you are smoking hot….. You remind me Megan Fox…. but much better version you has some brain…… Please don’t waste this look go to a casting for a big movie….. Anyway if you insist to explain math……. one advise before any new video start with the practial part first…… Tell the people what they can use this information for in the real world…..

• How she writes horizontally flipped

• I fall in love with you and your way to teach. Gracias for all.

• ุจุญุซุช ุงุญุงูู ุงููู ููุด ุงููุดุชูุฉ ูุงูุญูููู ูุงูููุชู ุงูุง ูููุง ุจูุช ุฌููููู ูุดุฑุญ ุฑุงุฆุน i want to understand the derivative and I found it great explanation

• Great video

• Thanks

• Finally I learnt something that I couldn’t understand in billion years studying in school in less than 15 minutes!

• Sorry to say this, but Math is more beautiful than you! Logic wins Skin everyday!

• Im so bad at math back then now im getting so much better ๐

• i think i hate my laziness when it comes to math more than i actually hate math. god bless these vids tho

• Great explanation!!! Iโve learned more with your video than I would an entire semester, thank you for that! Plus, that โinteractiveโ writing board makes everything even easier to get a grasp of all the concepts.

• Thanks.
From Morocco

• ๐ค๐ค๐ค๐ค๐ค๐ค

• My HS calc teacher was an a-hole. When he went around the class asking where we wanted to go after high school, in response to my stated choice of college, he responded:
“Oh, I thought they only take the best”.
Well, I made it to the college of my choice, because I went on a tear after that making sure I was accepted. But I have forgotten all my calc since then because it is only useful in certain limited occupations (which is why I am back here, prepping for a job interview). But it just goes to show:
1) Calc isn’t everything
2) If “they only take the best”, I guess QED that includes me – so suck on that Mr. Expert in something rarely useful
3) Notwithstanding 1 & 2 above, maybe Mr. A-hole is paradoxically partly responsible for my success – so…thanks…I guess.

• God I wish I had you as my Math teacher in high school & maybe I would’ve passed the first time. You explain its concepts very clearly.

• good

• Not only smart but you’re hot! Wow! I never had that in Grad School!

• Iโm tryin to learn Calc for fun, and these videos are extremely helpful.

• i really got many points that i have never had before thank you

• Getting more confused!

• who came here just to watch her?

• Sorry I can’t concentrate.

• Lost it at the end. Didn’t understand what this 6x actually means.

• I love this video. Oh who cares about the math? LOL

• Where new content?

• How did you get the 2xh?

• i am here to learn maths and watch your beauty

• Never saw any profs at my college that could teach calculus that looked this great.

• Thanks. Because of you I can now begin to grasp such complex Math stuff. Limits, Derivatives, Integral Calculus used to scare the hell out of me. Now I can deal with them; As student of Machine learning, I owe you a lot, Nancy.

• If you were my teacher i would sit in the front of the class

• The tangent makes sense but why call approximation the secant?

• Looking back, I know what the derivative laws are but I don’t have confidence in those laws unless I know WHY. That’s why understanding this is necessary.

• please translate to arbic

• o mogaka

• Thanks for the course so transparent and simply delivered.

• so we put the genome and match functions and reputations of repetition of every genome banding with sound formulation of sound and banding of dna molecules so we found that proper genome mixing so we got glucose molecules infinity unlimited ultimately ultimate food on and on continuously

• Nancy is so droll! I love her little jokes.

• If I had a teacher like this when I was a young man, I’d now be an aerospace engineer and not a garbage man.

• Your video’s are wonderful! Have you thought about doing videos related to linear algebra?

• This helps alot. Thank you so much!

• it’s truly remarkable that a woman can make a video on any topic and automatically get 100x the views of men. meanwhile, the dominant narrative in western societies is that women are somehow oppressed. hope you enjoy your undeserved success at the expense of innocent men. that’s what feminism is all about.

• Can we just love math without bringing in this other world nonsense! True lovers of the art do not see women or men, we see and appreciate the beauty of those delivering it, and the beauty of the discipline itself.

• @justanotherguy implying there aren’t men that do a much better job and people don’t only watch her because of her physical beauty. i’d love to live life without bullshit neoliberal propaganda like “international women’s day” (today) crammed down our throat by every major institution. until then, i’m going to call it how i see it.

• I love you miss nanci

• perfect presentation ๐

• Nice concept

• A derivative is a contract between two or more parties whose value is based on an agreed-upon underlying financial asset (like a security) or set of assets (like an index). Common underlying instruments include bonds, commodities, currencies, interest rates, market indexes, and stocks.

• I took calculus years ago. If my teacher had been this good at explaining it, I would have done much better. Now I actually do watch calculus videos just for fun. This was a great reminder of where the derivative rules come from.

• Im from syria . Thats very very nice

• Please teach me mat all day

• …………….

• Sexy voice ๐

• ลรถyle bi hocamฤฑz olmadฤฑ ki รถฤrenelim

• ://TSKO13;โ..Nothing sexy(er) than a beautiful woman doing math and programing๐ฏยฐ

• Wish I had a maths teacher like Nancy 45 years ago.! I Very nicely explained .It is like listening a poetry. My compliments .

• You’re so much better than most teachers.

• I came here for her pretty face and her curves

• I got lost … in her eyes.

• Thanks Nancy

• If I had a teacher like you Iโd be stupid.

• ็พ่ฒไธๆบๆงๅนถๅญ เญง(เนโขฬโกโขฬเน)เซญ

• Please do teach algebra.

• The teacher wanderfull!!!!!๐๐๐๐

• nice try… still boring…

• I dont know why I watched the whole video.

• The best part of these excellent videos is the cool sound made when the video is sped up.

• I feel like a lot of people do not watch this channel for Math….

• you look yummy

• nothing is better than Math

• What a superb explanation…. Thanks

• Do derivatives help explain why apes ponder their own existence or creator, or do they solve numerical equations?

• Now I realize why I love the math ๐โค๏ธ

• ยฟSo then, HOW THE HELL DOES SHE WRITE THE WAY THAT BOARD SHIFT’S HER SENSE OF WRITING?

• I donโt need to learn any math

• my trousers don’t fit so good right now…โฆโฆ…

• If h tends to 0, isnโt exactly 0, how come that you substitute 0 in the last step of the algebra? By doing that arenโt you making the distance between x and x+h equal zero? How do you calculate the slope of a curve by only knowing one point? Iโm not sure I have properly explained myself.

• I am going to say this you have don’t need to be so pretty to teach math hehehehheeh…..

• Wow!! I am not a math expert, but I know You + Me = Division by Zero Error. Wait… must have done something wrong. Let me try that again… You++ ME++ == FALSE. Damn! There must be an equation that is equal to HER+ME = TRUE. I should have studied my math and computer science! Damn! Again, HER/ME*US = Cannot Compute Invalid Entries. BSOD! Dammit! ๐

• I love derivatives so much ๐๐

• Maj stulej

• I always wondered what a derivative looked like….

• Nancy3.14

• ุจุญุจู

• Profesor + effects = do not pay attention

• yeah she is beautiful i am talking about the derivative. Great work!!! let me now check the integral one.

• Very helpful, thanks.

• Do you accept private tutor?

• I perfectly know what the derivative is…Idk why am I watching this for the whole 15 mins

• How to make those styled videos

• whait a minute? is that ASMR? caus i can t resit :c i want to sleep so badely in her arms

• I am a biology students but I don’t know why am I here

• Nancy… this is like ASMR I get easily distracted o.o

• I would never leave high school if i had her as teacher…

• Amazing

• Nice. I dropped out of calculus in college and never went back but I’ve always loved numbers.

• You arr beautiful distracting me to concentrate ๐

• Just dropping by to have my watching-a-beautiful-girl-writing-backwards fix. Bye!

• Damn she is beautiful.

• Maths is beautiful

• I hold a bachelor’s degree in engineering, but there is no harm in brushing up your calculus

• What is she writing on? Glass? because if so, she has to then write the mirror image. What is going on here?

• Great video

• Sexiest math teacher of all time. Great work, keep going.

• Que hermosa e inteligente es. Admirable. Como me enamora una mujer asรญ.

• i think she is writing everything backwards for us to see

• Do you have Spanish ancestors?

• You are quite possibly the cutest girl Iโve seen doing math

• Thank you madam.

• I would compute your second derivative the whole night just to see your curvature.

• Bravissima. Ps. che programma utilizzi per scrivere a video

• ะะธัะตะณะพ ะฝะต ะฟะพะฝัะป,ะฝะพ ะฑัะปะพ ะธะฝัะตัะตัะฝะพ

• Wao you are beautiful you wanna be my math teacher for ever๐ฉ

• You are beauty with brains.

• is anyone here to actually learn?

• I am from india good explanations

• Nancy’s Video was really helped me in Uni. thanks @NancyPi

• Can I get your whatsapp number ? I need your help to learn math

• Even if Donald Trump had a lim —> โ number of brain cells, He would still not believe this, and would rely on his hunches.

• Function: For every value of x, there is one and ONLY one value of y. It is just that simple.

• So cute

• Hi. What’s the practical real world implementation of this? Thanks.

• I’m here for an integral facial

• quand elle รฉcrit slope c’est bizarre on dirait une faute de frappe

• How did you move that linear line?! What magic marker are you using?

• cool

• have to envy those who just get it

• Half of the population here is for learning derivatives, while half of the population is for…… you know for what we are here.๐๐๐๐

• Ma’am aap kaha se ho

• you helped me a lot thank you so much Nancy

• Loved the explanation and recalled the faster way I learned 50 years ago.

• I bet she has a BBC boyfriend named Tyrone

• Thanks, you were incredibly clear!

• Im am sure plenty of men who are not in the least interested in calculus or maths are watching this ๐๐๐๐

• My season 4 is coming up in about 6 months. (I’m a very good sound engineer. I know maths also.)

• This helped a lot. Just finished the Machine Learning course by Andrew Ng (Stanford) on Coursera, and although it’s not strict required to learn derivatives, this helped getting a better understanding of how ML algorithms work behind the scenes (rather than just using them). Guess I’m gonna do a “Nancyflix” marathon.

• when am I gonna find a math teacher who delivers the real meaning of math that is related to our daily life routine ?! .I am not speaking about the numbers and all this stuff …but I am speaking about how do we teach our kids the intrinsic meaning of math…as an example for this episode, the teacher should have discussed the meaning behind calculating the derivative ….”why do we calculate it” …rather than just focusing on theoretical basis that everyone hate if he/she finds it difficult. please try to relate your examples to real life scenarios.

• Not meaning to be disrespectful, better than an intelligent teacher is a beautiful and intelligent teacher.

• Boy how much I love calculus๐คช

• If my calculus teacher looked like her I’d be a civil engineer instead of a CPA.

• lol

• Best Teacher Ever <3

• like like like like

• ะบัะฐัะธะฒะฐั ะดะตะฒะบะฐ. ะทะฐะฑะธะปะฐ ัะตะฑะต ะณะพะปะพะฒั ะบะฐะบะธะผ ัะพ ะดะตััะผะพะผ) ะดะฐะฒะฐะน ะฒััะพะดะธ ะทะฐ ะผะตะฝั ะทะฐ ะผัะถ – ั ะผัะปััะธ ะผะธะปะปะธะพะฝะตั)

• i have no idea what she s talking about!!but i watched all the lesson because …….

• I can’t see to the board because of you

• Wow superb but mam i asked that some books use Delta x instead of h but i like h because it makes simple

• If you explain the idea of integration then alot of thanls

• I didnโt know anything about this thing but boi sheโs fine

• YouTube recommended me this, sheโs not bad at all

• I use to hate math but now I love math because of Nancy.

• Hello Nancy , i need your help please give me feed back about your studio i need to use same ur techniques with my explanation videos

ekramyelkhodary.22@azhar.edu.eg
00201019836341 whatsapp
Thx alot

• NancyPi, ruin my life

• I would’ve been the high school topper if she was my maths teacher….. would’ve never missed a class…

• However, would you be able to concentrate?

• @Chien Yangthat’s a tough challenge lol.

• Im just here for the articles.

• 13:45 superfluous. The English word you are seeking is superfluous.
This is what happens when a polyglot reviews math.

• Talk to me math ๐

• That’s great! At 65, I had completely forgotten the first principles derivation, and thank you for reminding me!

• Very good

• Iโm actually in love

• I literally just watch her to appreciate what is going on. You don’t find many of these in the wild bois

• She IS teaching intellectual truth

• Good video

• Excellent explanation. How does a secant line become a tangent line. Not quite sure I understood the implication of how that helps us understand derivative.

• sweet nancy,,,,

• Hopeless….#2. I had a private tutor to get me through my a -level maths

• I love math because u

• โค

• Hi nancy ‘will you marry me?
So that I can clear my doubts in maths for all time…

• Horrible.

• gorgeous ๐

• This is 1000th comment here….
Very nicely explained… Great going Nancy….

• Very helpful mam ๐๐

• peace be upon you. you explained realy well.

• thanksssssssssssssssssssssssssssssssssssssssssssssssss…………………….

• Impressed that you can write so fast

• She’s great. clears everything up for me. ๐

• I Love You Ma’am.โฅ๏ธโฅ๏ธโฅ๏ธโฅ๏ธโฅ๏ธ Will you marry me???โฅ๏ธโฅ๏ธโฅ๏ธโฅ๏ธ๐๐๐๐๐๐๐๐๐๐๐๐๐ฅฐ๐ฅฐ๐ฅฐ๐ฅฐ๐ฅฐโค๏ธโค๏ธโค๏ธโค๏ธ

• please consider doing boolean algebra, this is some good stuff

• Beauty and brains…can’t go wrong…

• You’re too hot to be doing Maths

• My brain’s chain reaction at 7:47: ๐ง๐ถ๐ณ๐คฏ

• You broke the sterotype of cute girls bad at maths

• Love from india ๐ฎ๐ณ
I m in quaratine ,I hvnt cmplted my derivative ch ,and you let me know why it was f(x+h)-f(x)/h,,most of the channels are teaching how to use it but not how it works and why.

• Likes for the amazing maths lec in the building, under stood better

• Thank you very much for making math so simple and clear You are an amazing teacher

• IF YOU WERE MY TEACHER, i COULD HAVE BECOME A MATHEMATICIAN GENIUS MASTER THAT SHIT.

• 9:56 ๐is it wierd that i totaly get what shes saying. I was thinking about this in the begining of the video.

• Your so hot i wish you was my teacher be my favorite

• Thank you very much for your job. Your videos are full of usefulness and smartness, can you share with us how did you get accepted to the MIT& And can you give me a direction of what do I have to do to get accepted to the MIT?

• Excellent and amazing dear Nancy you are kind and sympathetic because your method of teaching show your passion to serve others. Tell me what is this we use this formula for derivative it is also derivative formula tell me.
Derivative=y2-y1/x2-x1=del y/del x diff between this and your formula of dervative in your video
Derivative

• smart girl

• Nancy, you are an excellent teacher. I learnt many concepts from you. Thanks. God bless you

• You explained this way better than any of my math profs did. Its been 15 years since I took calculus and I knew the rules to get the first and second derivative, but I didn’t know the underlying theory. Thanks.

• So a derivative works because we’re ignoring the fact that you can’t divide by zero?

• Did not get that limit rule, “how do we substitute x+h alt rest of it was a masterstroke very lucidly explained thmx

• Had to watch it twice,,, forgot to look at the math the first time

• But I did like Math, and your way of teaching it makes it fun, thanks your awesome

• weldon msm

• Hey, Instructor Ma’am I have a kind suggestion for you , Change your channels name from Nancypi ——-> Cutiepi . Kinda cute as you ๐and funny

• nice

• ๐

• nice mam of your method

• The image is mirrored

• Thank you miss for clearing

• NancyPi, Are you REALLY writing (and graphing) BACKWARDS?????

• was rechnen Aufgaben%4292 *75* 1141411 ?รท? 660225 !44144! &&&ร&&& #1# @5\$5@ ==***== ?????โฌ????? 1111

• Nice explanation

• Very Nice. Keep up the good work. I 100% disagree that Mathematics is a dry subject. Mathematics is beautiful.

• I got more out of this 15 minute video than 3 hours of studying class notes! Thumbs up & glad I subscribed ๐๐

• omg I’m in love

• Awesome explanation and detailed content which is easy to digest

• What are the uses of a derivative in the real world? Thank you.

• Very few people explain concepts in an understandable way. I mean, when you ACTUALLY UNDERSTAND what it is and why it is there. It’s easy to just DO IT because you saw 100 other examples but, what it really is, is what matter the most. This was amazing.

• Simply i fell love with your teaching nancy mam.super …..

• good lesson expontial equall how can calculateed

• Agora aprendo matemรกtica.

• Uy bb como es pa unas clases privadas

• so talented si host good job

• you’re literally saving my life. SO clear. My textbook SUCKS and is SO confusing. Thanks for helping me get through my homework. You explain things clearly and are not boring. Appreciate it.

• You look so beautiful in red ๐

• Very nice main M. N. Shukla (maths lect) from India

• Hi Nancy hope you are fine. Can I contact you by email ? My mail ID :ayazk021@gmail.com

• Who says Mathematics is not everybody’s job

• Unintentional ASMR

• SPANISH……..?……( โโฟโ )โก

• If I had a math teacher like that, I would study hard!

• Studying for my final! Great refresher, I used this same video when I was learning this concept earlier in the semester.
Its fun seeing the concept again after learning so much!

• You are more then good I like your mentored please how would be able to contact u

• ๐๐๐๐๐๐๐๐๐๐๐๐๐

• Nice job by a nice girl

• Nancy would be perfect for ASMR videos on mathematics. I think it will remove fears of mathematic on many students

• I love your videos. You’re able to explain things so effectively. I swear, my professor wasn’t able to convey as much info to me throughout an entire semester of precalculus and he earned three math degrees in grad school.

• And I don’t get why everyone keeps talking about her physical appearance as if it’s all that matters to them. If you’re not on here to learn math, what are you really doing? She didn’t post these videos so a bunch of desperate guys could come and drool and breathe on her neck. You people are just awkward perhaps? You like to make people feel awkward for no apparent reason? What is seriously wrong with you people. In all seriousness, get a damn life.

• Kepa kok dihitung 90 tdk 100 belum ada pembenan kok

• 1 lingkaran 100% you now

• Learning Math is so much better this way…

• I don’t like my x don’t ask y

• I saw the entire video. Wonderful. Anybody else noticed she was speaking about maths or something.

• I like how you explain everything with a calm and soft voice.

• you have good way for send formation ๐

• If this woman had been my math teacher i think my life would have gone a lot differently

• i love you

• Ok Nancy, I got stuck some at 10:59 . I can see *what* you did, I’m just not sure *why* . The way I explained it to myself is: f(x+h) (in the derivative formula) means the y value obtained from f(x) for a value (x+h), so to get that y value you have to plug (x + h) *into* the f(x) for each x present there, because that’s what f(x) would be *at* (x + h). That would be the *why* for the *what* you did.Your general explanations are so wonderful, and you seem to have all of them that are necessary, maybe that particular place needed a little more (at least for me)?

• Ok, so I see that using limits is how you get that formula for derivatives of powers, but it still seems arcane that you put into an equation a term (h), which you *know* you’re going to take out later by making it zero (or ‘going to zero’), and still get something useful!

• Thank you this really helped me

• ๐

• Med school is easier than this

• nyc # Pradip pradhan @12th Math

• I have watched this before. You explain it very well.

• I am now an engineer, but idont know why i watching this. Maybe I forgot what derivative is, or I am just single

• Love you Nancy, you are amazing

• DOES SHE WRITE ON HER CAMERA OR SMTHNG?!!!!!!!

• Your family name is Pi? My wife’s surname is Pi too! But we are Singaporean Chinese. When she attended uni, the lecturer always jokingly addressed her as Ms 3.1416

• Thanks for such a nice and easy ways to make hard things to simple ๐๐ผ๐ป

• Sรณ pretty! Love U! ๐

• why do we need derivatives if we could just draw a tangent line and figure out the slope from there? Awesome video btw.!!! Thank you!

• how do you make these videos? are you a wizard?

• Are you single?

• I especially like the new technical term I just learned to decsribe a rough estimate, “wonky.” Nancy makes technical stuff friendly.
Well Done!

• thank you so much Nancy.LOVE YOU!!!!

• Thank you so much for your tutorials, it really helps me when I was taking calculus 114. I scored over 80โs for my mid term exam and your lessons are very easier to understand the way you show different methods to explain things. I really appreciate your time and efforts

• I give up I donโt understand this

• Thank you, NANCY

• Extremely well explained. For the first time in my life, I am clear on the idea.

• Great work …

• Oh my gosh ๐ญ after hours of trying to learn this ๐ญ you made it so much easier somehow! Your formula is so much easier then the others my professors gave me!

• The way you moved that secant line to a tangent line and back with hand magic was so cool!!!

• Appriciate ..one of the easiest way derivative explained

• Eylene Pirez is way better looking :O)

• 11:50 for all the year 11 chisholm kids

• You are the best thanks alot

• Suberb mam I am great fan of your

• You are so beautifull

• I can’t focus on what she’s explaining ๐

• By just watching her videos I’m so obsessed to her and learning a lot because she reminds me of my teacher in algebra her pretty face the cheek bone the shape of the body and the soft spoken voice that always made my day she’s an engineer whoever the bf of this young woman he’s so lucky to have her๐

• I do not know I just come to see the teacher..

• Look forward write backward oh dear Nancy what are you doing…..

• Thank you madam…

• Shows entire sequence of steps for calculating a derivative.Me:Writes a few lines of code in Python ๐

• thank you! you’re a great teacher and you’re very pretty!

• I know it’s like a century later but if anyone sees this: Why is the limit 0? Minute 7:44

• Is that for high school students? High school math?

• Thanks mam for giving us all an MIT level mathematics education.

• Challenge accepted

• Focus on this question
Find derivative of sin4x sinn6x
Sin4x
The answer for this question is enough to show trigonometry derivatives method is nonsense.
Wondering when they will stop teaching this method.
I doubt if the girl in the video has a proper answer.
Somebody fooled her and is fooling 100 unknowingly unintentionally.
She is repeating like a parrot.
Ask her to draw a diagram and see for herself.

• That is the Frechnet derivative. The derivate that we ude in analysis.

• you better be a model๐

• Who else came here thinking GAL GADOT( Wonder woman) changed her profession๐คฃ

• just remember use the power rule

• You made it easier for me to understand ๐ Thank you for this video ๐