Implicit Differentiation

[@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

[@edilsonalmeida2383]

​ kmu🎉 hxgf rxaxxxxxaxaxxxfxxfxxxdxzxxaxxyxxxxxxxxxxxxxxxaxzxxdxxxxxxxxxxxxxzxxxxaxxxxaxxxxaxxxxxxxxxxxxxxxxxxxfddsddsdafssdfddsdddssdsfdsdddadddxxxxxxxdxxxxxxxxadxxxxxxxydyxxxxyxxyxyxxxxxxxxxxdxyxxxxxxyxxxxyxxxxxxxyxxxxxxxxzxyxyxxxxxxxxxxxxxyxxx̌xxxxxxxxd ajjjjpnnhm@@kriti4698bvrbbbbbbbbrrbbbcbbbcbcrcrbvgbb😢a j j. Bu VT navegar bbj

[@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

[@zareen331]

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

[@Jakob6174]

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

[@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

[@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

[@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?

[@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

[@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.

[@bfmvshinigami]

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

[@asemnafiz]

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

[@jackson8420]

The implicit and explicit analogy is nothing short of pure genius

[@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

[@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.

[@eduwhan]

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.

[@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!

[@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

[@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!

[@soffwhere]

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

[@nocturnalvisionmusic]

Relatable comment 💯

[@mmonty14]

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

[@KeepTheBeat411]

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

[@nocturnalvisionmusic]

Very nice statement. :D

[@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.

[@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.

[@pancakeofdestiny]

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

[@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

[@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!

[@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. ☺

[@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.

[@hummie3]

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

[@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 :)

[@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

[@turtletort1]

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

[@uajaksh09]

2018 and your videos still helping me

[@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

[@buey18]

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

[@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.

[@knowit3887]

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

[@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!

[@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

[@LandonHobbs]

Suddenly calculus seems incredibly intuitive! Thanks!

[@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.

[@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

[@kimmihamel14]

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

[@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.

[@bobthepianoman1993]

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

[@Jassy19981]

All hail khan academy

[@johnathonbegg1021]

Jasmine Bethel Hail!

[@cpillarie]

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

[@trinitaccad3066]

I'm jumping to the conclusion to guys who understand implicit differentiation can also answer all implicit questions of every girl out there. Very helpful technique right here.

[@ilpyrofreak1994]

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

[@altaffirdaus8696]

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

[@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.

[@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

[@Bryanj2222]

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

[@drhf1214]

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

[@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 :(.

[@nocturnalvisionmusic]

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

[@MatteNoob]

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

[@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!

[@Nutterbutterz95]

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

[@snowboarder12653]

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

[@asemnafiz]

That means when there is a change in that variable it will change the function. For eg. y is changing with respect to x means when there is a change in x, there will be a change in y. y is dependent on x.

[@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.

[@VironiaRoshdy]

Keep saving lives, Khan Academy.

[@louayomary]

sir you litterally are my teacher!!

[@cfarischon6]

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

[@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.

[@BrunoSoundFL]

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

[@farfigneutron]

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

[@kidart89]

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

[@Drid677]

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

[@BFrei46z]

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

[@Gazeta2nd]

Fields Medal. There are no Nobel Prizes in the field of mathematics. And, as helpful and awesome as Sal is, unless he has invented a super awesome theorem (of I'm not sure if he has,) I doubt he'd get any Fields Medal.

[@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?

[@Friemelkubus]

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

[@JFrameMan]

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

[@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

[@ihaveeys]

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

[@Ashenafi-k1n]

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

[@dhavalshah3881]

Such a brilliant and logical explanation!!

[@Shalashaska016]

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

[@backyardbeachbum]

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

[@ACDproductionsinc]

not sure how you do it but you make math interesting

[@trickingsessions]

i should be sending my tuition money to this guy!

[@drewsteps]

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

[@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

[@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?

[@jmbbala]

because Y is a defined function. in other words, y can equal many things. Y can equal x^2 or x^3 + 1. So its like youre deriving ln (x^2). this can be ln (y). therefore dy/dx of ln(x^2) is x * 1/x^2 or ln(y) = dy/dx * 1/y

[@VongolaTsuna27]

This helped me so much. Thank you

[@TomDabektv]

Time to change my major. Although on a side note I think you made this way more in depth then it had to be

[@yosefali7729]

you are a mazing dude making eveything simple

[@Homiloko2]

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

[@jmbbala]

y is a defined function. y^2 would be 2y * (dy/dx) because y is a function. use the chain rule.

[@md.ayaanahmed5152]

Alhamdulillah (Praise be to God) Sal exists. 😄

[@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 ?

[@michaelmascolino2262]

much better than a lecture.

[@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.

[@thevictorc]

y=x^x----> AWESOME! that was cool. thanks!

[@friendofcanisgirl]

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

[@JonathanClark11]

Thanks, you've helped me a lot!

[@camdrake10]

I'm sure you get this a lot, but thank you so much Khan.