MIT grad shows how to do implicit differentiation to find dy/dx (Calculus). To skip ahead: 1) For a BASIC example using the POWER RULE, skip to time 3:57. 2) For an example that uses a TRIG FUNCTION and the PRODUCT RULE, skip to time 7:20. Nancy formerly of MathBFF explains the steps.

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

Twitter: https://twitter.com/nancypi

What is implicit differentiation? Up until now, most functions you've had to differentiate have probably been written EXPLICITLY as a function of x, such as y = x^2. However, if a function y is written IMPLICITLY as a function of x, such as x^2 + y^2 = 9, you will need to use implicit differentiation to find the derivative dy/dx. The only difference is that any time you take the derivative of y, you must also multiply by dy/dx. The reason is that y is dependent on x. You can think of y as containing some x expression inside it, so

implicit differentiation is basically a special instance of the chain rule in which you must take the outside derivative but also multiply by the inside derivative, which is dy/dx in this case.

Here are the steps to doing implicit differentiation to find DY/DX:

1) TAKE THE DERIVATIVE OF BOTH SIDES, MULTIPLYING BY DY/DX every time you take the derivative of a Y: The first step is to take the derivative of both sides of the equation, with respect to x, but to attach a dy/dx if you ever take the derivative of y. For instance, to implicitly differentiate the equation x^2 + y^2 = 9, take the derivative of both sides with respect to x. On the left, the derivative of the x^2 term is just 2x. To differentiate the y^2 term, in this case first use the power rule to get 2y, and THEN, because y is dependent on x, you must multiply the term by dy/dx so that you have y^2 times dy/dx. Don't forget to differentiate the right side of the original equation as well, which was the constant 9, so the derivative is just 0. Your new, differentiated equation is then 2x plus y^2 dy/dx = 0.

2) GET DY/DX ALONE ON ONE SIDE: The third step is to solve for dy/dx, or in other words, to get dy/dx alone on one side of the equation. Next, DISTRIBUTE AND EXPAND BOTH SIDES if necessary distributing or opening up any terms that have parentheses. Then, if dy/dx appears in more than one term, get those terms together on one side and use the SIMPLIFICATION TRICK OF FACTORING out dy/dx from those terms so that it then appears only once on that side. Finally, DIVIDE OUT any factor that is currently multiplied by the dy/dx so that you are left with dy/dx alone on one side and an equation that looks like dy/dx = some other expression.

NOTE: Only multiply by dy/dx if you are taking the derivative of y. In more challenging examples like the second example in this video, you do not need to attach a dy/dx if you are just multiplying by y. For instance, when differentiating a term like xy, using the product rule gives you x times dy/dx plus y. Notice that in the second term from the product rule, it was not necessary to attach a dy/dx to the y, since you were not taking the derivative of y in that term.

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

Thank you!

I miss you. Please do complex numbers

do abstract algebra NO one is doing it properly on youtube

Fematika* hes a kid who does it very well

You don’t “do” abstract algebra, it DOES YOU!

@TaeKun Hey THANKS! I really need this for a cloaking device problem

@StarDagger Rihannsu Lol he helped?

Would be neat to see, but it’s probably too advanced and might not get enough views for it to be worth her doing. All of her stuff I’ve seen is at the Calculus 2 level at most, which millions upon millions study ever year. Most of the people studying abstract algebra are just math majors. It’s probably 1000 times less than the number of people that study basic calculus.

thanks nancy

NancyPi, when would this be used in real life calculations?

Physics, economics, basically every legit scientific field.

I’m so glad you’re doing so many more topics!

Great explanation!!! Thanks

Welcome back!. Gonna use this video later in this semester thank you 👌🏻

My best math teaching channel yet.

Dear Nancy, Love you .. you’re my hero ..

I like your half thinking/half explaining face–the rhetorical “does that make sense?” to the camera haha. Good job Nancy 🙂

Could you do a video on solving the derivative of the trig function by definition??? Thx!!!

Nancy solve word problem plss😔

who else’s y detector was set off at 8:01

Gonna dislike cuz why are you not my math teacher . SMH

Excellent.

Ms Nancy. I watch your videos from Iraq. Keep up the good work “You r my real math teacher”. I appreciate you

Me too ✌😂

And wich part of her body do you appreciate the most?

First off, Panty Sniffer is a pervert. Secondly, Nancypi only has a few math videos. I don’t think she can ACTUALLY teach you an ENTIRE grade in these few videos. These videos are meant to help you with your course.

@Panty Sniffer her brain

يا سلام في عرب وانا فكرت اني الوحيدة😂

are you right handed?

Thank you so much for making this cool video 😊

I. LOVE. YOU…….N A N C Y

There’s a fucking monster on my roof

>tfw math bff is dead because no more Nancy

Hi Nancy, can you teach us how to use the L’hospital’s Rule?

Hi, what happened to math bff?

Can u tell me value of tan inverse

Nah bless with some squeeze theorem

Laplace Transforms and Multiple Integrals would be really helpful.

Wow she helped me a lot in calm but I remember her old channel being something different

she changed channels LOL

14:08 “I just did a bunch of calculus, and it’s not my job” CLASSIC

@Jody Raiford thanks

@Chemist Me I know this might be radical to some guys, but she is a well educated woman who has a grand career ahead of her, an MIT grad as well as a YouTube phenom.

@StarDagger Rihannsu no shit sherlock, what is your point?

That’s what I thought she said lmao🤣

@StarDagger Rihannsu sounds to me like you are the one being sexist here. All of us here accepted the fact this isn’t her main job, yet you had the impression we thought that way. Dont try to sound morally straight when you lean buddy.

How do I get an in-person tutoring from you? 🙂

Thank you!!

Wish I were your student,nice keep up!!!!

Really helpful. Clear explanation. Stress to the point. Fantastic.

This helped me A LOT. Every university should link to your video (mine does, TU/Delft)

Thank you Senpai.

You saved me, I have a teacher who I never understand a single word from her and mathematics is my major.. thank you so much, wish you all the happiness !!

Your channel is so under rated! You explain things so well! I watched your Q&A btw! I am on the East Coast too and I loveeeeeeeeeeeeeeee pasta!! lol

Hey guys, we got a pasta LOOOOOVER over here!

Mackenzie Costner nhi degi

I always forget to factor to get only 1 dy/dx

thank you for sharing your intelligence, Nancy.

I am struggling with BC, and your video helped me a great deal!

Thank you is not enough to say, You really helped me in most of the things that I need.

Thank you Nancy

Hi ma’am Nancy your the reason why I always pass my exam in Differential Calculus. Thank you always😊

Could you explicitly give me your phone number? XD

Hahahaha you are legend

Funny

911

Get in line

Pliz help me this problem.

Let f(x,y)=c be an implicit function, show that

dy/dx=-fx/fy

I lost it when she said “y-detector” lol

When?

*will be amusing herself with this during the final on Monday*

(in buzz lightyear voice) ‘you don’t wanna be in the way when my y detector goes off… y’

Exactly

@Vaiebhav Patil 7:59

@Marc W. Thanks!

How can you write in reverse so well?

bro could you be so dumb

Hey, at least Cole gave an actual answer instead of being an asshole. Keep making your sad excuses of a foam gauntlets.

because shes left handed…

Never heard of sarcasm ? Or was your comment sarcastic too? Thats why sarcasm should only be used in real conversations…

@Michael Guariglia HA! Got him!

7:17 Creepy :O Btw, you make things look very simple lol xD Wish I could do like a pro in exams.

Invaluable. Your videos are invaluable. Thank you very much!!!

My professor is useless. He couldn’t explain this properly in over and hour. Thank you for making our lives easier.

Please upload videos about 3D Vectors. Getting destroyed in college.

Like Megan Fox, only with significant intellect and clear teaching skills, haha

She is beautiful isn’t she. Reminds me more of Jennifer Connolly though.

Ha!😂😂😂

you judgmental prick!

@Roman V. she has nasty toe thumbs

Her voice sounds similar to Megan’s but physically, she reminds me more of Angelina Jolie.

These videos are life saving.

Wow. I just found my online teacher. Thank you NancyPI!!!!!

how to did she get the x+1? by factoring the dy/dx? please help me..

Thank you!!! 😍😍😍

Thank you for your help.Now I can tell that I understand how…to do implicit differentiation. What is still murky is the meaning of all the stuff. Perhaps I only have to think more over it!

Thank you

OMG it was to factor out the dy/dx. Of course. Now I feel stupid after staring at this for 20 minutes. Nancy the witch! haha you and your sorcery. xD

Hello Miss @NanciPi, can you make video about chapter functions and De Moivre’s Theorem. I like the way how you explain it and solution in other videos. Sorry my bad language. Thanks

I only noticed her armpit

You are great! Thank you so much for the awesome videos.

I need help with this one problem that I have to solve with implicit differentiation. We have to find dy/dx and d^2y/dx^2. The problem is xy-x+y=2. For the first derivative I got (y-1)/(x+1) but for the second derivative I am completely stumped and its most likely due to the algebra. :/

this video is a GODSEND

Thankyou!

Police Sirens in the foreground @ 5:49

excellent explanation but please do some more complicated examples

Oh Ma’am You are the best …I REALLY love the way you teach Calculus

When the teacher covered it, it made no sense and seemed a beast of a concept! Now thanks to you it is a small kitten! Thank you!!!!

Don’t let this video distract you from the fact that she is sitting on the right not on the left!

Coming back after a year off math to find Math BFF gone was a sinker, you and Khan got me through my first two years distance learning. Thankfully I found this channel and get instant revision in your familiar cool, calm manner and slightly downward sloping, backward handwriting! Please keep up the good work Nancy, for us non-math built people, you are a God send.

Shout out to you paul, im in the same boat let’s get it

this video was AWESOME. you saved my life, thank you so much.

i thought she was writing with some whack ass form of backhand writing but then i noticed she is using glass in front.

thank you uploading your videos despite all those creepy morons in the comments!

thank you!!

seriously you are the hottest nerd there is seriously

She’s not hot. Lmao

She is hot enough to be a celebrity. I would comfortably use the word “gorgeous”

You rock

I would make you my girlfriend 🙂

This helped me a lot thanks!

you’re beautiful

How do you know Y is dependent on X?

Because we’re assuming X and Y here are defined in the common sense, where Y= some function of X (like when you plot on the XY Cartesian Coordinate Plane). It’s just that for implicit differentiation problems, you tend to not be able to explicitly write Y in terms of X, but the equation still gives us a relationship between the 2. 🙂

@Decaf-Math ASMR Thank you!

@Rockwall No Problem 🙂

Thank you for these videos they help so much.

How are you both exceptionally beautiful and intelligent? This seems impossible

Please Teacher Nancy explain absolute maxima and minima I’ll be thankful 😭🙏🏻🙏🏻🙏🏻

the max and min are where the graph of the function reached either the highest or lowest point possible, for example, f(x)=x^2 has a minimum of (0,0) but no maximum because both sides continuously approach positive infinity

Ya ben seni izlemekten dersi dinleyemedim be hocam 🙂

THANK YOU Nancy <3

THANK YOU

you say not taking derivative of y so you keep the y in 9:10. But you take the derivative in the y in 9:35. Actually why ?

I am in the mess

In the first one she is taking the derivative of x^2y according to the product rule(x.y = y’x+x’y), in the second she has to cause you have to take derivatives of all functions on both sides

Thanks mam

Thank you very much this really helped

Your videos make cramming for my exam much easier

Good job Nancy.You help me alot. You are so beautiful by the way 😘.

Hello. Just wanted to say your videos are helping me a lot. I’m really struggling in calculus, and your videos help. I was wondering, if you can maybe do a video on particle motion and optimization? Thanks

Which book is basic and best for differentiation?

you’re literally a life saver. thank u so much

This example are cheap can yu please Solve more complıcated ones

Thanks

you have SAVED my calc grade

Thank you I love you !

Hi I really like the way you explain. I wish you could make a full course on calculus 1,2 & 3 with quizes and all.

omg im a fourth year double math student at church teachers college Jamaica and damn i understand this in one watch thank you angel.

boys stop gassing her up, she is not even that hot…

😳😳

is she actually writing that backwards, or is it some camera play, if so what a talent.

In her profile pic her hair is parted the other way so she records backwards and flips the video during editing so we can read it.

@SRL Signs holy crap you’re observant mate

@SRL Signs No ! recorded normally and image is flipped as in photoshop.

SRL Signs lol just because her hair is flipped the other way? You can see that sometimes she slips up and doesn’t write the numbers as well as she does other words. So either her handwriting goes from good to 2nd grade level in an instant, or she’s recording normally.

Can you do a video for nth derivative?

This is the first time I have seen one of your videos Nancy. I very rarely comment on any videos, but I have to say that I think you are simply amazing! I am sure it must take so much concentration effort, being able to write everything backwards, while still keeping it all together and explaining everything in such a clear and calm manner AND never forgetting to switch between the two colors (every single time!). I have subscribed and am sure to watch your other videos as well as soon as they become relevant during my studies, Thank you so much for preparing and uploading this very professional video, much appreciated!

so im not crazy, how do you even do that and keep it together. writing mirrored is a huge skill

She’s not writing backwards. It’s a simple post-editing trick to flip the image. Lots of people doing videos with a clear board these days, so it’s a fairly well-known process. Other than that, you’re spot on that her video was extremely well-done.

@Nano Tellez Thanks for making me feel like a fool 😂 I really didn’t think about the option.. So Nancy is also not left handed 😉

On the second example. Can you add dy/dx + dy/dx to get 2dy/dx. then you divide the two? but it would make the bottom equal -2x^2. So what’s wrong with my logic? Please answer

does anyonw else get distracted at the fact she is writting mirrored. or am i crazy. like shouldnt the numbers be backwards to the camera. is she using a program to edit it to show correctly or is she actually writting mirrored.

Can’t believe it took me 4 videos to figure out how your writing. Good thinking on your part!

“So that should set off your “y” detector” lmao

love this video, it help a lot! thanks!!

Why didn’t you do the derivative of that other y? I’m lost 🥺😭

you are literally the only reason i am passing calculus thank you

It would help to write out the chain rule and show WHY this dy/dx crops up. Go just a little deeper.

You are the physical embodiment of girl power! Keep fighting the good fight!

Very beautiful theater!!!

Some topics in mathematics just make me so sad…

Parallel lines, for example. They have so much in common, but they’ll never meet!

I am a upcoming chartted accountant, , thanx for your video and for your beatiful face

more like an upcoming pervert

I have a fast way

pink color seems invisible on the screen…

most beautiful teacher of my life

I’m in a 4 week intersession calculus class and last time I studied algebra was 10 years ago. Your videos makes it so much easier to understand, the teacher explains based in algebra which has its value but it’s confusing to me. You speak in terms of calculus and that makes it so much clearer for me to understand. Thanks for the easy to follow explanations

It seems unsatisfying to me to have a y in the final answer. I would solve for y in terms of x in the original equation and then substitute it into the equation for dy/dx.

Wonderfully explained, Nancy. Thank you. I still need to view many of your earlier videos in order to establish the basics. Is there a particular order to your videos, going back to Pre-Calc ? If so, I would be most grateful to you if they could be listed and presented as such. If not, I understand perfectly. I’ll go back and research them. I am a subscriber and was also a subscriber when you were Bffmath. Many thanks to you, Nancy. And thanks for explaining techniques with such precision and patience. You’re amazing.

Thanks so much for helping 😀

SHE WRITING BACKWARDS?!

I think I just felt in love :O

THANK YOU SO MUCH. Hopefully I pass my calculus exam tomorrow

thank you!!!

wait are you writing backwards???

But Y, so serious 😛 hahaha

How do you answer ×= sec 1/y ??

I find myself randomly staring at you instead of focusing on your teaching…

Nancy > my calculus professors at uni.

Thank you for doing these.

Do calculus 2 for the love of God. Please! ❤️

Hey Nancy, could you do a video touching on related rates? Thanks!

You kill it every time!!!!!

Hmm, my maths teacher will call me his favorite because of this…. Lol. Thanks a lot

Just Saying, She’s writing backwards…

🤣🤣🤣🤣 and it’s not your job but I appreciate the help. Thank u

You teach better than that professor dave guy

thanks ❤️❤️❤️!

On problem #2 why did you apply the product rule like that?

I thought product rule is

f(x)g(x)=f'(x)g(x)+f(x)g'(x) so it should be -(2xy + x^2).

John Smith because addition is commutative……..?

“Y detector” 😂😂😂…anyways thanks…simple enough

Thank you so much. your second example really touched up on other areas like product rule and algebra. Does iD involve things like quotient rule and log or natural logs. I’ll try to find out that answer before my upcoming calc test lol, if you or someone else doesn’t get to it before.

I honestly can’t thank you enough Nancy. my professor is a small smelly balding man who shows his butt crack every time he tries to reach for the top of the white board, he coughs every 30 seconds (he’s a heavy smoker), and he’s all over the place, literally making it up as he goes. Your videos are pleasing in every way… perfect audio, great video quality, great examples and a clear purpose to everything you say, do and show! You make calculus stupid easy, because it is. Everyone who thinks math is hard either didn’t try hard enough or had a poor instructor.

Help me please

Let f(x,y)=c be an implicit function, show that

dy/dx=-fx/fy

Nancy Pi you are amazing, thank you!

Thank you Nancy

she is just so fucking sexy. ridiculous. something in the water.

THANK

I laughed way too hard when you said Y detector. I don’t know what I am transforming into, but I am not fighting it.

You are so helpful. Thanks.

god bless you

Prettiest math tutor I’ve seen

The problems that kick my ass are like….

If xy+5e^y=5e , find the value of y” at the point where x=0

And

Finding dx/dy of:

cos(xy)=1+sin(y)

second one,

cos(xy)=1+siny

xy=arccos(1+siny)

x dy/dx + y= -1/(1-(1+siny)^2)^1/2 * cosy dy/dx

dy/dx ( x + cosy/(1-(1+siny)^2)^1/2 )=-y

dy/dx= -y/ ( x + cosy/(1-(1+siny)^2)^1/2 )

Where did you get such questions xdd

and finally

xe^y=x-y

im guessing you need to find dy/dx?

y=x-xe^y

dy/dx= 1-(xe^y dy/dx + e^y)

dy/dx=1-xe^y dy/dx -e^y

dy/dx(1+xe^y)=1-e^y

dy/dx=(1-e^y)/(1+xe^y)

there you go

@Warc Arden I got them from webassign.net

@Warc Arden thank you so much for your time! I have a final coming up, so these will be very helpful🙂🙂

nvm the second one is wrong, I thought you had to find dy/dx

let me fix that one for ya,

cos(xy)=1+siny

xy=arccos(1+siny)

differentiating with respect to y,

x+y dx/dy = -1/(1-(1+siny)^2)^1/2 * cosy

so

dx/dy= -1/y(cosy/((1-(1+siny)^2)1/2) + x)

there ya go

(Yeah its just the reciprocal of my original answer but just wanted to do it again with respect to y since thats what is meant to be done)

Hi, i don’t know how often you make videos a week or month but I have my second calc test next week. May you do a video on related rates?

I Ned that too also optimization

Same

1:42 I thought that sound was my stomach.

thanks

Nancy pls do a video on related rates ;-;;;;;;;;

wonderful teacher, thank you!

Your voice is just relaxing

I guess there is a little mistake in your summary. Instead of “…y^2 times dy/dx”, it should be written: “…2y times dy/dx”.

Wow she’s really good at writing mirrored and backwards wtf

Unless they just flipped it in post

Thanks mam

I got an A in my Trig class because your videos helped me so much ! I’m taking calculus now and I’m so happy to see this!!! THANK YOU

Diana get ready to get F

@abood she cant get an F since Nancy is here

@Akin Pedro She can only get the D now

Wow all you guys are such assholes

Great videos always! Super helpful as a Calc 1 student to see other ways of thinking about and doing derivatives, limits, etc! 🙂

Yes

Thank you!!!!!!! i have been trying to understand this for weeks and you explained it great

violet from Incredibles??

Thank you so much…It was so helpful!😊

Wow Nancy you explained what my math teacher couldn’t thanks a lot

I started watching your video sets on calc just before I started a course on it. Very helpful and easy to understand. Thanks a bunch!

I’m doing MIT open courses, this time I got books a pc and an Imac.😁

Can you make a reverse chain rule tutorial please?

holy shit i finally understand

Excellent explanation

ily

Shouldn’t there be a dx after the 2x when differentiating x^2+y^2=36? Meaning we get 2x dx + 2y dy = 0

No, we are differentiating with respect to x here.

thus derivative of x^2 with respect to x is simply 2x.

derivative of y^2 with respect to x is the derivative with respect to y first and as per chain rule, then with respect to x which is why we write it as 2y dy/dx

Your videos are amazing. keep it up.

My goodness Nancy. You teach way better than KhanAcademy. Thank you so much ❤

You are a gift

Thank you so much for the well constructed video and patient dialogue that walks us through each step! This is very appreciated, you’re a great internet teacher!

It’s very easy tour trick. You write as always then mirror the whole video. That is why appears to be you are goofy

THANK YOU!!!!!!!!!

Excellent your teaching method is very good thank you.

THANK YOU

like

at 12:46, Nancy’s marker magically goes from a pink marker to a black one…

omg thank you ❤️

Thanks for your help.

We are using chain in every question of differentiation ex. d(X^2)/dX = 2XdX/dX

Thanks for video

Does anyone hear a faint siren sound in the background ? Or is it just me ?

I have a graph with me. Which have only phase of 180 degrees. But have a length of 1000mm. And a maximum height at 90 degree of 1mm. How can I find out the equation.??

I’ve never been able to work out how she is able to write backwards.

EightLeafClover she doesn’t

@Huda Mursal What happens then? How does she manage that?

She mirrored the video

U r soooo hot

Great video. Thank you.

Can’t we convert the equation into y=√(36-x^2) and then explicitly differentiate it?

try to do it.. and compare the results 🙂

derivative of y=x^2 with respect to ln x

@Abhinav Jain thank you for your reply.

Why were you so shy while recording the video by the way thank you very much

Thank you so much Nancy !

Nancy. Thanks for taking the time to take your time. The biggest problem with seated lectures is that the teacher knows the material so well that they go through it really fast. I never have time to fully comprehend what’s going on. Going slow and explaining your steps is so incredibly helpful!

You are very beautiful

I never understand English but I watch your videos

I can tell by your perfectly constructed English sentence

@Shahil H Matlab

useful – thanks

I love your videos

I just got a bullshit PTSD and ADHD diagnoses so that I can go into the retard testing room and cheat using my TI Nspire CAS.

Sir Lynchalot the fuck

worlds hotest math teacher

Hi

How to simple power defferentiation ?????

you are amazing thank u

THANK YOU FOR THIS

How is Nancy writing like that? Is she writing in mirror writing or is it some computer trick! It’s blowing my mind.

I just love the editing like how you use a mirror for teaching purpose 😍

You killed the romance. Now she’s just another girl that writes normal.

x4y2+sin(y)2=0 plz solve this on ur videos “4,2,2” r powers

Youre just awesome

u r really impressing teacher

God bless u

You only think you’re impressed but then you notice she’s doing it all while writing backwards.

Thank you so much for explaining it very slowly as if you know you need to teach it to someone dumb like me . which is a good thing . helped a lot!

An excellent teacher.

her face flushes around 10 minute mark in these derivative series. I don’t know if it’s stress or something else lol

Best help for my diff equation

Oh my GOD.

A Teacher should be an actor like her.

The rain lands mainly in the plain.

Total and partial differentiation please

Thank you!

Perfect female specimen does not exisss

Alright, you’re my new math teacher, can you please do functions(domains, ranges,types[esp. as written in thomas calculus ed 13])?

It would be much appreciated since I just started at university. Thanks

i love u, thank u

Lose the pink marker. It is not showing up well on your board. Stick with black, blue and green markers!

How are you able to write on the glass board from the rear?…good work

Ramy G i’m kinda thinking that she writes it facing her and then they just flip the video so that it faces us now

LOVE THE WAY YOU MAKE IT SUPER EASY TO COMPREHEND…THANK YOU SO MUCH NANCY.

implicit differentiation? pSSHSHSHSH!!

haha

This is more correct

Y^2+x^2=36

y = (36_x^2) under root

Derivative of( 36_x^2) under root is

(_2×)/2×root of (36_x^2)

_×/root(36_x^2)

You are awsome!

My eyes only focus on her not on her notes. HAHAHAHA

how tf do u write backwards

You’re indeed a true hero. Please have more and more example solvings. Thanks very much, Nancy!

Thanks nancy!

What about if it is written with respect to y? Means all that has x term will be multiplied by dx/dy?? Need help please

could you please do a video on how to find points of intersection between a tangent and a curve, im so lost…..

Hey Nancy what does 2x rhyme with 😘.

she is so clever

Thank you!!! Finally I understand implicit differentiation!

You actually can solve it without implicit diferentiation, look:

First we need to isolate Y:

x² + y² – 36 = 0

x² – 36 = -y²

sqrt(-x²+36) = y

Then do the derivation normally:

dy/dx = 1/2*sqrt(-x²+36) * -2x

dy/dx = -2x/2*sqrt(-x²+36)

Since sqrt(-x²+36) = y, we have:

dy/dx = -2x/2y

dy/dx = -x/y

Implicit Differentiation is a short cut for solving multiple intermixed variables. Your way is fine for non-intermixed terms, and longer. Besides, there are more than 1 way to solve certain MATH problems.

Great way

Not only is she writing left handed but she writing backwards too

at 7:16 i got a little spooked

thankyou

Thank you so much. 😍 Your so Genius and Sooooo beautiful. 😍😍😍

Saw this tuesday for the first time and panicked, read the whole chapter and had no clue. Just watched this for 14 minutes and it’s clear as day. Thank you so much!

God Bless You!!!! My calc teacher isHORRIBLE and this saved me

am I THE ONLY ONE who can’t see the pink written stuff?!

This video helped but would have been better if you did a problem that had a x^2y^2 in it

Hey Nancy pi how do I find the second derivative using the implicit differentiation?

Here’s the start of my question: xy+y^2=1; solve for y”

Sister pls do some videos on complex numbers and permutations and combinations. Your way of teaching is very good and understandable thanks for it.

Thanks the test is tomorrow and you just helped a great deal.

thank you so much you are the only who is thorough and clear enough. you helped me so much!

Nancy you r beautiful and thank you. I want to know about vector

Thank you so much Nancy you are making things a lot easier for me now. BTW you are so beautiful as well, I almost lost concentration by starring at you hehe. Watching all the way from the land down under (Papua New Guinea).

❤❤❤❤❤❤❤❤❤❤❤

frustrates me that it appears as if she’s left-handed but righting backward right-to-left for the viewer. could so much skill really be possible? in need of a behind-the-scenes.

Christian Evans 99% sure that what she does is write on a transparent board from behind it just like anyone would and then she simply mirrors it when editing the video so that the writing is right

Nancy, You are a gem!! Are you born again? Bless you a Thousand times

very beautiful woman with brain thanks a lot

Thank you so much!!

Wonderful Teaching🤩

I don’t know if this is a silly question…Are you writing in reverse? or on a mirror? I’m getting distracted with trying to figure out how you’re writing and not paying attention to the content.

Your videos are just basics

So kind of wastage of time, try covering some concepts for JEE exam

Great video 👍

This is super amazing. I was actually struggling in Implicit Differentiation.

thanks nancy

Thank you Nancy so much, I had to stop the video and write this comment only to thank you before I finish watching the video. This was something very difficult for me to wrap my head around it.

THANKS MILLIONS.

YOU DO AMAZING TUTS.

watching your fantastic videos from Ethiopia

Thanks madam

Warning! 13:29 “this looks really innocent.”

Plz tell me what is derivative of y

Are you writing backwards?

Hi,thanx,thee be incredible,now GOD BE BELOVING OF THEE,THY TRUTH BREATHES LIFE INTO LIFELOVE OF THE RELARTIVE TRUTH OF SOME SYSTEMS,SEE 3D,GRID IN LARGER 3D GRID,DFRNT AXES MEETING POINPARRICLE,THE PAIR 3D GRIDS,THART THE d/D,DIFUSN/DENSITHRUM OR FISDION/FUSION,OF EACH 3D GRID,WITH DFRNT RELARTIVE dt,d^2t,of 2 grids,as well as cenchienrum,functions dascribing trajectory of each axes meeting POINPARRICLE,both breathes in rhythm,or dissnanc,inflection exhaustion,into dot,dt=>,thus die,death of system,Pi best seen as dmtr of thick theory straight line rotarting 185-190,370 degree to ensure circle true,if plane dmtr rotartion flart,RELARTIVE smooth,but theoretical,as 3 dfrnt RELARTIVE,3 x 3D grids see in 11d,to 12d,but see axes as each dfrnt rartRARTIO RELARTIVE MAESURE system reliabilithrum,as tuning drum alters with thin,or thick artmaosphere,thick,low pitch,similar with thy functional wissum,breathing truth,Pi varium,inside,ARROOUNDING,scribe circle ⭕️ dmtr longest str line scribing circl,thanx,bliss, XAMBUNJILOM

Thank you

9:09 NO. WAAAAAY.

SO THATS why we don’t mess with the second y…. omg. *kaboom*

i cant tell if ur sarcastic but I don’t get this part at all help lol

@Yousef , she’s using the product rule to differentiate x²y. Remember the product rule is f'(g(x)h(x)) = g(x)h'(x) + g'(x)h(x). In other words, the first function times the derivative of the second, PLUS the derivative of the first function times the second function.

So, with x²y the first function is x² and the second is y. (Remember that y is just shorthand for the function y(x)). So we have the first function times the derivative of the second: x²(dy/dx). PLUS the derivative of the first function times the second function: 2xy (note: no differentiation of the second function here).

In total we have: (d/dx)x²y = x²(dy/dx) + 2xy.

Example:

Implicit differentiation of 3x^3 + 5y^2 = 15:

3x^3 + 5y^2 = 15

(The differentiation is implied)

You’re a really, really great teacher. Very clear

@7:18 she stares into your soul…

I’m doing Calculus online through WGU, and your videos have been a major game changer in how to understand this vs just reading about it. Thank you!

The whole video i just watching that she writing in left hand in mirror form….😑

And enable to understand any implecist. Stuff🙁

I admit NancyPi’s math skills are superb…..BUT IS NO ONE GONNA SAY HOW AMAZING IT IS THAT SHE IS WRITING BACKWARDS AND FACING US???? THAT IS TRUE SKILL.

Thank you. Helped me on the final

4:07 – Why do we “have to” use implicit differentiation here? Why can’t we get it inti the form “y = …” by subtracting x^2 from both sides, taking the square root of both sides (hmm, how would the +- be handled during the differentiation? We would possibly get two results, right?), then differentiate normally?

~ 8:40 – The derivative of y with respect to y is one, but with respect to x it would be 0 (if it didn’t depend on x, that is).

كيف تكتبين كذا اتمنى الرد 💙

عبدالله ما أتوقع انها تعرف تقرأ عربي، بس أكيد استخدمت لوحة شفافة للكتابة.

Can you teach me long division. Mamm

Nicely done! How about doing a video on Fourier Analysis?

Or bezier partial differential equations ? Thanks!

Thank you nancy. For your help in learning the derivatives

Nice explanation. Love you

How can you not e understand Math, when a sexy & intelligent woman like Nancy is explaining it to you?

I wish I had this available when I was in college.

sugar britches i want you to balance my check book

you’re not a math teacher, you’re a model

4:11 You can in fact do it explicitly, its just easier to do it implicitly. Anyways good video!

do you edit your own video?

Stunning smile!

She sounds so bored. “So this is X negative = kill me now”. Explain how you’re more boring than a pure mathematics text book?

You should do a Netflix series

Beauty with brain

❤️❤️❤️❤️🌹🌹🌹

This was incredibly helpful. Thank you so much for making this simpler.

Liked, very understandable

So difficult to concentrate becoz she is too good looking

Nancy, are you doing this in a mirror?

Miss NancyPi writes backward with the left hand, amazing

She fine

very beautiful and intelligent. if i proposed, will you accept me

THANK YOU!!!

May God continue to bless you

With me discovering this channel, I’m gonna pattern calculus easy. Mans gonna secure that B grade

that B = BAG

She speaks energylessly

They say beautiful girls don’t understand math. They must have missed this Nancy

Hi Nancy!

how can you right by left hand and it is a mirror reflection, omg good practice

omgosh I’m cramming for my Calculus midterm. Why didn’t I find your channel earlier in the day! <3 thank you!

y^2 + x^2 = 36, how is the answer -x/y help? Interesting

When you have ” x^2 + y^2 = 36 ” why can’t you simplify this expression to “y = x+6 ” and “y = – x -6 “? Like can’t we just simplify and then differentiate?

Can we use y’ instead of dy/dx?

just notice, how is she writing the opposite way lol?

but what an explanation

thank you so much

Thank you so much!! I feel like I’ve made every mistake, but I get it now, thank you for such a clear and helpful video!

hey Nancy I love you and I have some questions, for question 1 why not just put it in the form of y as y=(36-x^2)^1/2 and is your last name really pi or you just want to be irrational 😉

WHY AM I WATCHING THESE MF ADS IF ITS NOT YOUR JOB

THANK YOU

thx woman

Your can write backwards cause your left handed. That’s the trick

Its so rare to see beaury with brains

Corona Virus screwed my cal1 class and this fr did help

Thank you very much!

Now I’ll just watch it again so I actually understand what she’s saying…

thanks so much!

I really feel like we could use a blooper/outtake video from you.

How the heck do you write backwards so neatly

I enjoy your videos and all but I wish you would write the dy/dx in a darker color than pink like purple or something else that will be easy to see.

Thank you

Please diffrenceate both side

this

X^2+y^2=k^2

Help!

How do you solve

y=x^2 / y^3

Beauty miss

why do you keep sighing like your being held at gunpoint to teach

Why can’t you rearrange a function like x²+y²=36 as y=sqrt(36-x²) and then use the chain rule by writing that as y=(36-x²)^0.5?

Also I liked your video, it did help me.

Okay I tried it and it works, I guess it’s the same thing

Wooohoooo today is my last day of Calculus ever and I believe I will finish with an A :)))) thank you for your videos! Most math videos are so boring!

u got me thru ap calc queen

Who is watching this video in 2020

How can you write in reverse that’s AMAZING

So, she’s writing from right to left. I really like her commitment

It’s just flipped, lmao

@s!CKman k

You’re so hot and sexy

Can you please share a video on how to solve this

Xsquare + Y square ÷ X square – Y square = a ( a is constant)

Great video.

I’m going to always remember ‘it should set off your y detector!’ LOL funny but thanks for the reminding tool haha <3

Thank’s a lot, it helps better than the one with my mothertounge tho

Are you writing everything in reverse on a glass plain that you’re filming through?

Good

why hasn’t anyone acknowledged the fact that Nancy is writing inside out

its mirrored after

@Google User I think he meant that she’s writing away from her body

Right, she’s writing to her right which would go away from her body. Then it’s flipped

@Google User She’s writing right to left ..

@Trevor Starr yes but if you mirror the image it becomes right to left

I need help to find the general expression of X belongs to the vector field manifold which satisfies : [ d/dx + d/dy , X]=X

You could also use Partial Differentiation as a short cut for Implicit Differentiation

I’m not looking at what you are writing, just look’n at you

Thank you! I might pass AP calc now

Can you please make a video on intense or some of the hard problems related to integration ??

great video

Thank you dear Nancy 👍👍

Thanks Nancy

You truly are a gifted mathematician

God Bless You

Ur videos r very helpful

I want to marry her.

She’s beautiful tho, so now i kinda wanna study

5 mins and 48 seconds there’s a police siren

When my teachers teach : Oh Calc is hard

When you teach : tbh thats pretty easy

Plus my teachers arent bad at teaching maybe i find it easy now just coz in re watching what i earlier learnt

This makes so much sense now… Thank you Nancy!

You’re so cute

Nice

You are very smart, and surprisingly nice to listen to… Thanks for this video it helped a lot helping me to start to understand what to do, also I never knew you were double jointed til I seen your pinky bend backwards at the start of this video. 😛

Thanks Nancy!

what i really want to know is how does help me in life? when do i use this? or have i been right all along and postsecondary education is just a scam to steal your money, break your soul and erase your humanity in preparation for the professional world?

Right explanation

These videos are awesome, I was so confused but this cleared it up better than the 3 hour lecture I was in! Thank you

Nany I reallylike your vids i suscribed liked and hit the notification belll you make it look so easy

Love your explanations, very clear and concise, making math, especially calculus, easier and fun to learn! Much appreciated

Thanks. I wish they would hire you to translate Pearson textbooks instead of the incompetent lizard people who eat there own feces and use Google translate 30x in a row before defining a theorm or anything important…

thank you for smiling nancy 😀

am now a lecturer cos of you, thanks my tutor……NANCY

I did a problem like this 23 years ago. I think it’s the same one I totally don’t know how to do it anymore. A co-worker and I had to figure out a hole size and I told him we could use a Bering to measure the hole size. He didn’t believe me at first. Them I drew a picture of the bearing sitting on top of the hole and said if we can get the height of the Bering we can get the hole size.

He then was amazed and said oh ya I know how to do that!

Thank you

This was a big help thanks prof pi