Implicit Differentiation

[zjzortiz]

Wouldn't the answer be e raised to the answer we got seeing as the natural log was taken of both sides?

[vaccumenhancer439]

Duck shitty quack quack pick up a shovel go bobby go well uh working work. Life is so easy with calculus :)

[fisigagmail]

Your are just amazing.

[TheWuFinancial]

If I was in prison with this guy I would take a shank for him.

[OmarAle14]

@TheWuFinancial ;)

[cactusbottom]

woo midterm tmrw, thanks alot khan!

[ditto56789]

FUCK YOU MAN YOU ARE A FUCKING GENIOUS. SHIT THIS MADE MY LIFE SO MUCH EASIER.

[H0oLIgAnSsRo0lMaRrSz]

@DarklightALBANIA that is the actual chain rule written out. that's how its stated in my calculus book.

[SupaMangoTofu]

Dude your making me hungry -____- that's the last thing I need while I'm cramming for my limits derivatives test at 4am

But thanks you helped me a lot!

+1 subscriber for u

[DarklightALBANIA]

I don't understand how you get from 06:00 to 6:20

What did you use ,I can's see where the chain rule is used there

[ihaveeys]

thank you !..I finally understand whats going on in class thanks to u :)

[xoprincess94xo]

@Swax6302 LMAO you just made my day!

[Megatr0n12]

just for the record girls are always implicit and guys are explicit

[nicola1984patriots]

why did you take the natural log but not base 10?

[beer94]

anyone else see gay squared in the upper righthand corner? that must be really gay

[MrILIVEWITHMUSIC]

@beer94 hahah 

[ABCba5tard]

y do the ln but not log base 10 ?? i dont get y

[bernardmvella]

@ABCba5tard It's easy to differentiate ln I guess?

[Swax6302]

i wish implicit differentiation was as easy as being able to tell if someone was hungry...

[benzbubblecat]

whenever I search for a math concept, I look for Khan's blackboard

[oglow100]

@benzbubblecat sooo tru haha he deserves a nobel prize i swear!!

[farfigneutron]

Thanks so much. Sharing knowledge like this is a beautiful thing

[backyardbeachbum]

you and derek owens should run for president/vice president 2012. i would vote for you in a heartbeat. 

[AlexandraMercury]

THANK YOU!!!

[BorealNeal]

7 people failed out of calculus

[SM10101010]

Dude what software is this??

[Mrcyberboy18]

Can you do derivatives of logarithmic functions? PLEAAASSSSSEEEEE!!!!!

[malejames90]

7 people still don't get it, after they watched the video.

[supercalifragilismic]

i envy those who's only taking calculus now and seen this video. saved you a lot of headache and confusion

[buhoman3]

pleaaaasssssseeeeeeeeeee do 2nd derivatives of implicit functions!!$#%#^&*%^%

pleassssssssseeeeeeeee

[Homiloko2]

OMG!! Now I understand!! Thank you so much Sal, we love you.

[TheRuth101]

I wish I would have known about this in high school.

[ParanormalEnities]

This is the first time that i find math interesting and simple!I always hated math but now i understand that i always hated math because my math teachers were so fucking boring!! Love your videos you are a life saver.

[JFrameMan]

thx, this helps. idk why books pick the worst way to explain this

[SehamArad]

arrghhhh..too many letterrsss...???..totally lost..then again i havent finished watching the video...

[HunteronX]

Thanks for the help!

[cmillerthuggin]

are you jesus?! haha thanks for the help man idk where i would be in calc without you

[blueskycadet]

THANKS FOR THE HELP : )

[bfmvshinigami]

I like how Sal teaches in simple terms while also going into sufficient depth into the particular subject. Great job.

[flarefiragax]

Thanks Sal, that was very, very useful. My textbook didn't explain it too clearly so I came here and now I understand it completely.

[w15h0na5tar]

when i tell my friends i get math help from youtube, they look at me like i'm crazy, but this is truly very very awesome help/tutoring

[DanaSiew]

total awesomeness.

[mewosh]

"these" are not essentially fractions, but a type of notation, strictly speaking.

[kidart89]

"You'd get y squared is equal to, what, 19? Uhm those numbers are weird..." Hahah Sal, you are the man!

[cakezyum]

love your explanation ^^

[elsalfo]

I LOVE YOU!!!!!!!!!!!!!!!!!!!!

[louayomary]

sir you litterally are my teacher!!

[pamBBB]

You are a very good teacher. Explaining the difference btwn implicit and explicit helped!

Also, your voice sounds very nice.

[pompeuh]

great explanation

thank you so much!

i think you could do some good teaching math, because all my teachers are not so good explaning..

[KOOL2011]

Salam o Ailkum, thanks for the video :)

[MathMeeting]

Great video on implicit differentiation. I also have a video with two examples that explains how to take the derivative implicitly. Click on the channel below to see all my videos. I also tutor online.

[fonbinsmonbin]

@MathMeeting stop spamming these vids pls

[jsfb9]

Sal, I love you in a "no-homo" way.

[pontis0]

Good explanation, but maybe do a version in non-Leibniz notation? I find it hard to understand, and I'm sure I'm not the only one.

[Krizbo]

@pontis0

Totally agree with you. I don't have any idea what is going or how to solve implicit differentiation.

I think it is b/c of the dy/dx that is confusing me.

[Diviniteee]

I have an assignment due in about 8 hours where I need to use implicit differentiation but I have no clue how... This helps me so much; thanks!!!

[Falandorn]

Your brain reminds me of a box of monkeys khan, every now and then one gets out and runs away, you have such a broad range of knowledge you cant help but running off at a tangent sometimes whilst explaining its great :)

Thanks so much for these videos they are amazing!

[mmonty14]

you just saved my calculus career. THANK YOU! THANK YOU! THANK YOU!

[danky123456]

isnt the end problem logarithmic differentiation

[64z]

Ha wow!! this is the first video from khan academy that i actually Don't GET!! am i the only one confused!?

[dytryn09]

You are a math god!! i love you.. no homo <3

[deadboy000]

oh why oh why would someone dislike this video? ignorant idiots.

[mrsnipes99]

@deadboy000 very ignorant idiots....this helps me with all aspects of industrial engineering

KHANACADEMY in general

[OnyxCode]

see OnyxCode and try to decipher it !

[mzb86]

omg i wish m calculus teacher would watch ur vidoes and learn how to teach us, and not be so confusing! i love how down to earth and normal " calculus" sounds when u teach it!

[davvigtu]

11:58: You can do it explicitly too. x^x is equivalent to e^(x ln x), so set y = e^(x ln x) and just use product and chain rules.

[slashgashshorty]

lol its almost 3 am my test is in like 6 hours but yo you make my prof. look like an idiot man, thanks!!

[jajaman1993]

Summarize a whole chapter in 15min....Thank you

[SFCNRocks]

Just a thought..

If you say: "I haven't eaten in a long time and I would really like to eat something"

What kind of retard needs to do work to figure out that you are hungry?

[Sylvanas17]

i never get bored watching ur vids xD

[teluguc]

wow seriously this made it so easy.... only if schools hired teachers taht could speak english, and especially in univ.

[teluguc]

honestly, schools need to get teachers that can speak english! and i especialy mean colleges.. UB sucks for CALC!

[7025Nikhil]

hey he did much o.a in dis vedio........

[tIs4gatorbait]

"boy it would be nice to maybe eat something.." i cant be the only one who laughed at this.

[snowboarder12653]

i am so grateful for the kahn acadamy. thank you for posting videos 

[DotDMod]

Wow, I'm not sure if anyone else noticed this, but he's pretty damn dexterous with his mouse writing these problems.

[robertliu4499]

@DotDMod hes using a writing pad

[DotDMod]

@robertliu4499 I thought he was also, but the mouse is constantly moving as if it never leaves the pad.

[Kirajc]

Thank you... didn't really get till I saw it done here.... THANK YOU!!!!!!!

[Juriello]

WTF IS THE POINT OF LEARNING THIS?!

:Sigh: Thanks Sal, even though it's still confusing.

[WaRSPiRiTUK]

Count how many times he says derivative and I'll give you a fiver. :)

[idster7]

why doesn't the derivative of x^x just equal x((x)^(x-1)) (times 1)?

[hyein101]

"I am hungry"

Now I'M hungry o_o

[ghostman515005]

thanks for saving me (:

[fullshtop]

you re awesome

[kami645464]

6 people missed the like button

[planondeath]

1:40 - 1:50 LMFAO!!!! thanks for video though, it was very helpful! P.S. your way good at writing with a mouse.

[armadillodude2992]

Much thanks and appreciation! Your video was very informative! Thank you!

[comeonnowsugar]

Thank you so much!! This video has been ridiculously helpful!! This is the only thing that has stuck with me all semester and I feel really confident about knowing!! I'll definitely be using your videos more next semester!

[petadd]

nice stroke order for your boxes--i suppose you know/are learning chinese? or maybe another asian language that follows the same stroke order rules?

[cfarischon6]

Thank you so much!!! i get it now! Calculus is ruining my life this semester!

[jiemo]

thanks for the help!!

[ObamaSucks12345]

Mr.Marks at roosevelt licks mens asses all day long

[AronL91]

This is really sick explanation! Thanks for the help + keep up the awesome videos!

[apartfromthispoppunk]

Top analogy. haha

[KeepTheBeat411]

You, my friend, are the integral to my derivative. THANK YOU!!!

[Seedofwinter]

@KeepTheBeat411 This guy LOL

[Anonie324]

@KeepTheBeat411 Hahahaha.

[xDaisyCharm]

You have a really nice voice.... :)

[BrunoSoundFL]

Awesome videos, your saving my life in Calc BC. Thank you.

[pass135]

Going back to that side bit you said about the circle, if the gradient function ends up being = -(rcos@)/(rsin@) then it will be = -cot@, am i right? and if so can we say it is true for all circles of radius r, with centre origin?

Very interesting btw, love how you promote an intuitional understanding rather than simply stating the rules.

[debit256]

Can you do with with newtons?

[kiatmac1]

OMG MARRY ME

[ixdani]

I learned calculus AND English!

[Seedofwinter]

I still don't have the intuition of it, I'm really trying. I could follow the steps and Ace my tests, but I want to under stand it. Maybe it will come to me eventually.

[Adamwallace5]

@Seedofwinter same here!

[starefossen]

Thanks a lot, this was really helpful!

[jc4zbay]

You rock Sox!!!! Thanks a ton. I have a more complerte knoeledge of implicit differentiation now. Be blessed!

[guyboy625]

bloga

[LandonHobbs]

Suddenly calculus seems incredibly intuitive! Thanks!

[locusinbloom]

Man, you rock! Why couldn't my calc prof. have explained it like this?

[JayDee98765]

Man, i'd buy you a beer or something if I could :)

[EezyMacaroni]

WEAK. Do some implicit differentiation when you've got to do the product rule of the independent & dependent variables. This video is for simpletons.

[whisper012]

@EezyMacaroni That's the whole point fucktard, it's a video for people who don't know what implicit differentiation is.

[xXxWat2K7sonxXx]

For y^2 the dervative nortation is incorrect, it should be d/dy [y^2] not d/dx [y^2] as you differentiation the variable repect to y. And the answer is dy/dx = -x/y

[cuatro175]

thanks mate, now i get it :D

[chocolatebubbles91]

THANK YOU SO MUCH!!

[ouchimdead]

yay i can skip school!!!

[opticalwinter]

Thanks for this! Much appreciated! Your videos are all amazing! :)

[dcourtn1]

salmon khan!

i appreciate all that you have done.

[mathdude26]

unfortunately the 'formal' way the math teachers teach calculus is disgraceful. when students are only taught a grab bag of techniques to memorize, and this is their only experience with math...well no wonder y so many dont get math.

im sure if art or music were taught in the same manner many people would similarly 'not get it' as far as art and music goes.

but im so gld there are people who post these kind of vids.

thanx

[rockclimber21]

is anyone else cramming the night before the AP test? lol

(thanks, by the way, this is perfect)

[jaylay734]

@rockclimber21 yes omg thats exactly what i'm doing right now hahaha

[edwebo]

@rockclimber21 hey, what is the AP test? I'm from NZ and i'm not familiar with it. Is it for university?

[spelldragon93]

@edwebo No, they are tests created by the College Board (the company who makes the SAT) corresponding to a series of college preparatory courses offered to high school students in the US and many other countries. The test is not for university, although a certain score on the test may qualify for college credit, but those policies are decided exclusively by each individual university.

[mknelson100]

I am amazed... after 2 full semesters of college calculus (which means 2 different professors and 2 different TAs) I still didn't understand Implicit differentiation. Who knew all it would take was 16 minutes on YouTube and now I completely understand it! Thank you SO much!

[Fencefeet]

Too bad every teacher can't be this thorough. You're awesome man. You make my entire school's math program seem like a joke. Great lessons.

[mattmc6]

Great videos. You have seriously made me pass physics and calculus this semester with flying colors. You make my teachers look terrible.

[krishmu3]

THANKS SO MUCH!!!

[1001014]

Let g(y)=In(y) and we are given y(x)=x^x , let the z function be z(x)=g(y(x)) hence

z'(x)=g'(y(x))*y'(x) so its 1/y*y'(x). In Leibniz notation: 1/y*dy/dx. so he is using the chain rule. I got this from his previous video in the series, check it out! You're great Sal!

[vivian333999]

u r insanely smart

[lesly3343]

thanks!!! great work...

[MrBedofrd]

can u do slightly more complicated problems

[beregorn90]

Thank you sooooo much!!!

[Dijineroo]

Thank God I found you :D

I don't have to fail maths anymore ^_^

[kami645464]

This is quiet confusing, but if you listen to Khan properly you will find out that actually everything he says makes sense. Just pause the video a lot of times and you will all understand it. This was the same with me. I was having problems understanding this, but after pausing it a couple of times I now understood it finally.

Thanks soo much Salman!!!

[katanphetamine]

after 13:00 you kind of lost me...third time watching it past that point. I guess it was bc u said things without writing them. I'm a bad listener lol.

[katanphetamine]

ok, it wasn't that. I don't understand how that's the chain rule when there is no outer function on the left...seems like u got the derivative of them individually and just multiplied them.

[dagonlord32002]

there is no outter function but u have to take y into account of a function of x so u do the dy/dx. In the question if its xy do 1+yy'

[1001014]

@katanphetamine the outer function g(y)=In(y) and the inner function is y(x)=x^x.

[crunchies444]

You need to teach my calculus teacher how to teach calculus...Or at least hit her. Oh yeah and thanks for teaching me what Implicit Differentiation is

[angelsarah7]

i dont understand how the chain rule is involved.. was it defined in other videos with leibniz's notation? i only remember it as f '(x) = (g'(x))(h'(g(x)) .. how does that relate to implicit differentiation?

[Dhanaviir]

@angelsarah7 look at derivatives 1-9

[russianasian]

I have a test in a few hours. Thank God I found this. Yay for procrastination!

[patilnikh]

"it's the other way around" I meant that video should have been first then this.

[patilnikh]

WATCH ''More chain rule and implicit differentiation" FIRST then this.

It's the other way round. he said it himself.

[ShogunAssassin4135]

This pisses me off. I cant believe youtube is charging a buck for videos people upload to share with others. They should be free for download. Good video.

[bmxforlife6392]

@ShogunAssassin4135

it is free, with a little software

[timetraveler3797]

Bandwidth costs...

[JonathanClark91]

Thanks, you've helped me a lot!

[JMasterfizzle]

Lmao click the download button, and look at the license.

"No Derivative works."

I found this hilarious

[Darklink224]

thank you

[joeyjoey1122]

I disagree, I think it is clear. I think this video is very helpful.

[Adore121]

Very helpful video - thanks!

[CineOT]

sorry but this video is not clear

[Hawkallica]

this is as clear as it gets

[kleinehenkie]

Thanks from the Netherlands

[FoxyJD22]

sal to the rescue!

[smk252]

Awesome, thank you

[babygurl25392]

thanx this really helped me

[Hagbard420]

"Its sometimes fun to just think about things."

[illestdesimc]

why did u assume it changed to an implicit function after changin to lnx

i dont understand how you can tell if its now implicit or explicit

[xUltimaProductionsx]

The equation became implicit as soon as he took the ln of both sides, since it was no longer just y = x^x.

[slawsonCA]

Is there a mistake at 14:10 ? You are using the product rule. but aren't you suppesed to do: [the first times the derivative of the second + the second times the derivative of the first]?

[shananay]

That's the same thing, it doesn't matter which way you do it. [First times derivative of the second + second times derivative of the first] is the same thing as [derivative of the first times second + derivative of second times first]. Write it out your way and you'll see you get the same thing as in the video.

[Nutterbutterz95]

"Boy, it would maybe be nice to have some food".

Love the analogies.

[erikae93]

7:27 lol see the top right corner... gay^2 XD

[rinwhr]

gey

[MrFloydc2]

is this equivalant to higher maths ?

please reply?

[EcinPC]

No. This is calculus I. You can do this as early as junior year in HS, but some people take it their sophmore year in college. Highermath would be things that only math majors take. Junior and Seniors at college. Im taking linear algebra and differential eq soon. Those too, aren't higher math.

[TheRedLady1430]

y' also dy/dx?

nice video

[cookieeatbird]

yup

f'(x) = y' = dy/dx