Implicit Differentiation

Taking the derivative when y is defined implicitly.

[@mycommentpwnz]

I would like to take a moment and thank the gentleman (Sal I believe) who took the time to make & upload these videos. I've been watching these videos since college algebra and a lot of these videos have helped me SO much. You are the best tutor ever. You are free, explain things extremely well, have a pleasing demeanor, and you're smart as hell. I've never struggled in ANY collegiate course. Hence, I never had to ask ANYONE for help. Then I found myself struggling a bit in Calculus and Pre Calculus, and I was either too proud or too arrogant to seek help. Thankfully, I found these videos and they pretty much help me through all the difficult math courses I'm taking. So, THANK YOU SAL. You are the FREAKIN best!!!

[@treytadel3502]

IKR!!! Couldn't have said it better myself

[@yashaswikulshreshtha1588]

True but my mushy brain can't process intuition and concepts beyond pre calc level. I am in calculus and feel like I wanna drop out fr

[@mycommentpwnz]

@@yashaswikulshreshtha1588 You can do it. It just takes time. I ended-up getting a B+ in Calculus. And, it was hard for me too.

[@yashaswikulshreshtha1588]

@@mycommentpwnz I see yeah but it gets toxic when you want to aim for A+ because you need it for financial support.

[@mycommentpwnz]

@@yashaswikulshreshtha1588 Eww. That's pretty gross.

[@Liam-bp2rm]

THANK YOU FOR BEING A BETTER TEACHER THAN THE ONES I PAY THOUSANDS OF DOLLARS EACH SEMESTER TO LEARN FROM

[@kriti4698]

Well you just pay them to check your paper and not for learning.

[@leonmuller8475]

Kriti Priya Sadly that is true, even though it shouldn’t be that way

[@Jaloloype]

When Sal is doing the same question for your HW. I FEEL BLESSED.

[@terrapins]

Or, your teacher is plagiarizing

[@megaprime67]

plagiarizing math equations? I dont think you know how this works.

[@tyrannism5648]

Dedoria I trademarked "y=x". Like, it's mine now. Don't use it or I'm suing

[@Jakob6174]

"It's sometimes fun just to think about things..." - Salman Khan

[@zb14847]

i really love the fact that you explain the theory behind it. in school we literally got told to 'just put a dy/dx next to it'

[@lemonadepie9631]

zareen same!!

[@happycakes1946]

In College this is true. LOL

[@mohammadmujahid199]

normally thats wat gr 9,10 or 11 teach, cuz we dont rlly learn the basic foundations of calculus, the teachers just wanna rush the syllabus

[@montef246]

i like how in depth he goes bc instead of just saying "do this and you get this" he explains why it works and the math behind it so it helps me to learn it and make connections

[@justinkolbek9258]

your voice is so relaxing yet focusing at the same time

[@imrozzahan7328]

Justin Kolbek , you are gay.

[@justinkolbek9258]

Aw come on

[@yuvrajdhillon1036]

@@imrozzahan7328 y r u gay

[@soffwhere]

"Boy it would be nice to MAYBE eat something.."

[@emilielee3378]

Exam is tomorrow. I'm so dead.

[@WoodyIsAwesome54356]

same

[@WoodyIsAwesome54356]

Who just liked my comment

[@sadicanrot2226]

Same

[@adriancres8598]

Same

[@momonde8707]

So, hows academic life?

[@azharrazak3462]

Hello 240p, my old friend

[@gonzaloayalaibarre]

The "p" stands for "pal".

[@uselesssanity]

Azhar Razak nice to see you here again

[@rayhanmansoor2951]

Hello 1080p, my old friend

[@jackson8420]

The implicit and explicit analogy is nothing short of pure genius

[@bfmvshinigami]

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

[@KeepTheBeat411]

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

[@nocturnalvisionmusic]

Very nice statement. :D

[@alihammad4213]

I would like to take a moment and thank the gentleman (Sal I believe) who took the time to make & upload these videos. I've been watching these videos since college algebra and a lot of these videos have helped me SO much.

[@Jassy19981]

All hail khan academy

[@johnathonbegg1021]

Jasmine Bethel Hail!

[@cpillarie]

KHAAAAAANNNN!!!!!!!! KHHHAAAAANNNNNN!!!!!!!

[@treytadel3502]

Somebody *Please* GIVE THIS GUY A MEDAL!!!! .........Sir, there are no words that can justly justify the gratitude I have towards you and all the Khan Academy family for all the effort and real aid you guys give out everyday to people all over the world. I'm currently studying at University in Jamaica; a first year student that just completed his first semester, and thanks to YOU specifically, I flew through Calculus 1 with flying colours...so, all I really wanted to say was thank you. Thank you soo much man. I really really mean that. THANK YOU

[@mmonty14]

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

[@DGVFX]

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.

[@drhf1214]

"I dont want to make my videos long that you get bored." Oh Sal. :)

[@asemnafiz]

A nobel prize in peace for bringing peace into the minds of million students by helping them all around the world.

[@christopherchiaro2328]

You are absolutely amazing. I have watched your chemistry and math videos and your ability to convey an idea is unprecedented. Thank you, Sal.

[@altaffirdaus8696]

Hey! How could yo mange so many topics and subjects? Amazing!

[@onefive10]

Thats exactly what I'm doing my teacher tried to teach this today and I had no idea what she was talking about. I watch this video and I'm enlightened

[@EnriquelgIesiasVEVO]

I haven't studied at all, I have a test in one hour, I watched this video and I already understand this lol! God Bless u Khan!

[@pancakeofdestiny]

duuuuuuuuuuuuude the thing you did with "g" finally allowed me to understand this on a conceptual level. You da boss

[@Nutterbutterz95]

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

[@uajaksh09]

2018 and your videos still helping me

[@wtfisit25]

So I learn the basic concept of Pre-Calc from my teacher, then I completely understand it after I watch these videos. Thank You so much!

[@eduwhan1]

I came here dreading implicit differentiation and wondering if i'd get it. And in the first 2 minutes you had me go "is that it!?". Wish I had you as my lecturer. You'd dispel all my math fears just with your approach. You're really one of a kind. I thank you and please don't stop.

[@LandonHobbs]

Suddenly calculus seems incredibly intuitive! Thanks!

[@Qurdall]

IB Calculus test in the morning. And I've had a substitute for the past month. And to top it off, it's the last assignment of the grading period. This video was so helpful! Thanks so much!

[@MatteNoob]

Thank you for this! You are the best math tutor on youtube!

[@itsme1232620]

i'm a third year engineer student learning diff q and i had forgotten about implicit diffrerention in calc one, much appreciated refresher, thank you, this clears a lot up.

[@turtletort1]

These videos helped so much after I fell asleep in calculus class!

[@haynaku98]

my cousin suggested this channel and I'm thankful cause I found this. I really need this. Thank you very much for the effort. ☺

[@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.

[@hummie3]

Why is there not a million views on these videos! Spread the word!

[@kidart89]

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

[@Bryanj2222]

great video. I was stuck on implicit differentiation thank you for this video

[@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.

[@gFamWeb]

I'm still waiting for him to say "My name... is KHAN!" :)

[@tejasdevgekar1154]

Thats rude man!!

[@tejasdevgekar1154]

Thats rude man!!

[@gonzaloayalaibarre]

He's the great Khan.

[@knowit3887]

Video was made 12 yrs ago . Now helping a small 11th standard student to learn the maths for ai.💙

[@ilpyrofreak1994]

anyone else just ignore their calc teachers at school and learn from this guy?

[@kimmihamel14]

You, sir, just saved me from failing my calculus exam. You're my hero :)

[@user-74652]

I know that this video is really old, but it has helped me a lot in understanding implicit differentiation. Your videos have really helped me in understanding the concepts from both calculus and linear algebra that I did not quite understand. My professors are good, but it is great to have that extra resource when they are not available.

[@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

[@ankitaaarya]

Wow this comment is 8 yeaes old

[@MrPrunecandy]

Khan as opposed to a regular college calc lecture is so much better because of one thing.... EXAMPLES. Fucking hell, my professor lectures gives one example of the easiest problem of the material imaginable and then leaves us with homework with stuff we've never seen before. THANK YOU KHAN

[@synchronizedstereos4148]

5:36 when you take a girl home and find a bump in her pants

[@SatvikReddy123]

lmao

[@VironiaRoshdy]

Keep saving lives, Khan Academy.

[@dhavalshah3881]

Such a brilliant and logical explanation!!

[@buey18]

5:00 onwards was gorgeous... infinitely better than any teacher i've ever had.

[@1LHerne]

dy/dx = y' d/dx is really just an operator, it just states the derivative in terms of x (but not of what function). If you apply the operator d/dx to the function y you get dy/dx

[@bobthepianoman1993]

Calculus 1 final in 8 hours... you are saving my life.

[@NoellieOREO]

I have been so lost in my calculus class and finally things are starting to make sense :) thank you! I have a huge midterm next week

[@MDSHAMIM-qg4lp]

Ok n ki h7uujhu7vh h.o9

[@mrz2263]

THANKYOU SO MUCH, I HAVE A TEST NEXT WEEK AND I WASNT UNDERSTANDING THIS BUT NOW I DO! I LOVE UR WAY OF EXPLAINING CONCEPTS

[@adityagarg1838]

U are a true genius mentor and a saviour. Thanks you so much for your valuable lessons that have helped me immensely... LOVE YOU! P.S. - And I feel that this channel is so underrated!! This should have at-least 45 thousand thousand million subs.

[@louayomary]

sir you litterally are my teacher!!

[@user-np7rn2rc5t]

Thank u for teaching me, if it wasn't u i wouldn't understand alot of math and economics questions

[@BrunoSoundFL]

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

[@Homiloko2]

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

[@snowboarder12653]

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

[@friendofcanisgirl]

Thank you so much, I was really confused but this helped a lot!

[@BFrei46z]

Somewhat helpful. I am going to have to go back to the vid on Exponential properties, However. Thank you, Mr. Khan.

[@chuckles1252]

my teacher didn't really say what implicit or explicit means, he just showed us how to get an answer without explaining why we get the answer. thanks :)

[@farfigneutron]

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

[@JZXKenny]

Sometimes I wonder what is the point of school when you can learn everything online. lol thank you for taking the time to explain this!

[@PhatPhunkyPhatso]

Why do I bother getting up at 6 in the morning to be able to get to a calculus class with a teacher that you are 100x better than, if I could just wake up when I want and watch this whenever I want and understand it first time?

[@dcourtn1]

salmon khan! i appreciate all that you have done.

[@nocturnalvisionmusic]

1:35-1:55 implicitly stating I am hungry is really neat exampleship :D

[@Shalashaska016]

Much appreciation on this. Always had issues with Tangent Lines where I'm just given the equation and a point.

[@kenramos9991]

thank you very much. you've been a great help

[@ihaveeys]

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

[@westonwbrown]

Flipping genius, thank you so much

[@MathHacker42]

I think that the formula dy/dx=y(d(ln(y))/dx) should be taught and used widely, because it easily deals with taking the derivative of functions like x^x. It comes from the chain rule and the identity d(ln(x))/dx=1/x. It can be easily used to prove the product/quotient rule and power rule. I don't know who else has stumbled across this, but to me it seems like it should really be a fundamental part of calculus rather than an obscure little trick that no one has ever heard of.

[@stvntastic5164]

“I just became a KZbin partner so my videos can be longer”

[@cfarischon6]

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

[@vpatel7777]

That moment when you finally understand a math concept

[@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.

[@trickingsessions]

i should be sending my tuition money to this guy!

[@AnnieBerkley]

"It's sometimes fun just to think about things"

[@ankitaaarya]

Are you alive? After 6 years of commenting this

[@sarak.8859]

@@ankitaaarya 7 years now

[@SalimHamood1]

@@ankitaaarya are you alive after a year ?

[@hang321hk]

so clear=] keep posting these kind of videos

[@drewsteps]

Khan, you've been my teacher for an entire semester.

[@VongolaTsuna27]

This helped me so much. Thank you

[@Drid677]

Me getting bored listening to you're videos? Never in a hundred years!

[@michaelmascolino2262]

much better than a lecture.

[@vkshkmr101]

He(Sal) is a genius. He might be a PhD. or something I guess. But he starts it from very basics. In every lecture, he made me feel that he knows only a little more than me.

[@Yourztrulydaboy]

shit makes noooooo sense

[@matebah]

I hate this so much

[@hannahmacintosh1123]

Truth

[@JonathanClark11]

Thanks, you've helped me a lot!

[@ElectronNinja]

Thinking about my Calc-II teacher from last semester....yeah pretty much LOL. Always good to come back to stuff that hasn't been used in a bit and come out of left field at yourself with it. Unexpected things are remembered best :P

[@TenzaBurabura]

@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.

[@jaiso434]

your a saviour. thanks so much.

[@Friemelkubus]

One does not simply get bored with khans video's.

[@keez2007]

But i won't go into that, we're just learning about impicit differentiation, but it's sometimes it's fun to think about things Man, i love this guy

[@lallimircci]

Mr Khan, you are such a great and talented teacher. Why didn't my professor explain that we should take derivative of y simply because we must apply the same transformation to both sides and to all terms of the equation?

[@isak885]

I'm learning a lot from your videos. Last year i scored 86% on my Standard Level maths exam in the IB. I've decided to go further and do Higher Level maths during the last year at IB. Thank U. I did however find this video in particular very difficult to follow :(.

[@qualquan]

Simple definition of implicit function: Multiple dependent variables of a single independent variable. For example if X is the single independant variable having 2 dependentvariables namely X and Y. Sort of opposite of partial functions with a single dependent and multiple independnt vaiables Besides awkward use of chain rule. So when finding say dY^2/dX by chain rule one should show all the steps. So initially we should write d Y^2/dY and not dY^2/dX. Then one can easily see that dY^2/dY = 2Y and dY^2 = 2Y*dY. Then dividing both sides with dX we finally get dY^2/dX =2Y*dY/dX. No need to use the confusing dg

[@cakezyum]

love your explanation ^^

[@raphael056]

Those who disliked can't process what Khan is saying= EASY STUFF

[@cactusbottom]

woo midterm tmrw, thanks alot khan!

[@Sylvanas17]

i never get bored watching ur vids xD