Chain Rule Examples

[@ftit5893]

Normal teachers: explains the simple questions and leave us with the hardest Khan: explains the hardest and makes us feel that calculus is fun

[@r4fa3l59]

But calculus is fun, indeed :/

[@aaaaaa-rr8xm]

@@r4fa3l59 these q isnt even that hard

[@sagnikbiswas3619]

Facts

[@Javiertennis2044]

My teacher said we'll have to do 12 functions inside of 1, though. Lots harder.

[@BB-co9jn]

This site has improved my grades immensely for several challenging college courses. Thank you.

[@sterlingarcher3981]

B E I take calculus and vectors in high school

[@dytn959]

Sterling Archer cool no one cares

[@JamesTownsendJian]

@@sterlingarcher3981 r/IAmVerySmart

[@selfrighteousduck9151]

@@JamesTownsendJian bet, I am an 11 y/o who learned this for fun without problem, redditor

[@TheAlmightyNivs]

My prof is great but hearing someone else explain it is just that much more helpful.

[@smartconjurers2509]

The highest quality content available in the lowest quality graphics!!

[@GreaterDeity]

Seriously, I would fail calculus if it were not for these videos. I cannot tell you how large of a service you are doing the student community by posting these. You have my deepest gratitude. I'd be happy to donate resources for your services here!

[@singularityeh6002]

I swear I will donate as soon as I can as you deserve it khan academy.

[@deltaschool4302]

did you donate now ? after a year ?

[@bobfrasure8436]

​@@deltaschool4302 All in due time.

[@sufiyan2920]

Did you donate?

[@sarahkaveh7739]

Did you😁

[@grantklenske9888]

did you donate tho

[@eron6362]

Back in the days of 240p...

[@rayhanmansoor2951]

Back in the days of 1080p....

[@dhruvupreti5120]

@@rayhanmansoor2951 though they have now come back!

[@zeyadalabdaly3393]

To be honest it looks much more fun, entertaining, and captivating.

[@apexpredator9021]

In this example you have applied the chain rule once. In some tests it requires you to apply the chain rule until the inner function is at its simplest, so very basically you are left with one x and a number. That is why its called the chain rule: because you can continuously apply it until you reach 0.

[@sanchitabardhan7301]

So basically is the derivative = derivative of the inner function * exponent! ?

[@kimmarch90]

I have been noticing this too. My professor takes steps so much further and expects us to do so also. :/

[@No_BS_policy]

First order derivative. Only higher order derivatives require iteration of the chain rule.

[@oldprofile17]

@@kimmarch90 It's been a year but if it still confuses you, it makes more sense when you think of the exponent*thederivative has some constant (A) and apply the d/dx Af(x)=Ad/dx f(x)=A*f'(x) rule. Then repeat the chain rule.

[@VBSyd]

The derivative of f(x) in the first example looks more complicated than f(x) to be honest...

[@bartoszprzybysz5416]

I've been out of school for about 5 years now. Thinking about going back tor a mathematics degree I never finished as a Computer Science major. I have to say, Khan is more coherent than most of my university professors I've ever seen!!

[@Bloodsaberxy]

i have never had a teacher this great... bless you man, you're just amazing at what you do

[@1010nedim]

im spending a fortune at university and learning 1/5th of the information i learned in this video big ups :) and a BIG thank you!

[@Primitive_Code]

Good video but you should add natural logs, logs, trig fcns as well, that's where the chain rule raps a chain around your head.

[@kream013]

i agree with all these people who find this video soooooooooo helpful....i was trying to study this in my calc1A text book and the longer i tried to understand the chain rule the more confused i got. this video makes it so clear. thanks a lot.

[@vashistaditya4150]

Mr. Khan, you are a beast! The way you explain is amazing.

[@bayekofsiwa5847]

Thank you always, Khan Academy! You are the best!

[@TheEliteBalla]

You sir, are a hero above all heroes.

[@ChrisGilbert1]

I have spent days trying to learn this and you taught it to me in 10 min. Awesome videos. Thanks for the help.

[@LittleMissSpunky]

You didn't confuse me, very clear!! thank you. I am a maths tutor and I usual only tutor year 10 and bellow but I was recently given a year 12 student who "cries when it comes to methods, the whole class does" (His words!) this will greatly help me get him to understand this!!! so thank you again!! :D

[@steelguts777]

These videos are amazing, I love how you are direct and straight to the point wasting no time at all. I am definitely recommending you to all of my friends :-)

[@shadowking255]

you are just changing the world man.That is something you should be proud of

[@pro4skill]

amazing... I watched these videos non-stop, and now I'm going to be ahead in calculus! (I'm in precalc) Thanks so much!

[@lotslepy]

the world needs more people like you, sal.

[@indirasrinivasan9711]

+Khan Academy I just wanna say you are doing a marvellous job explaining the content of all your videos. You are the reason I could intricately understand certain concepts. Thanks a lot!! xoxo

[@xzxz619]

A kid with rudimentary math skills can learn this!!! Are you a some sort of math GOD?

[@party360Li]

i been struggling in calc this whole time n i tried my best to learn my text book n the more i tried the more it confused me but after watching your videos for d first time itself it all made sense...THANK YOU SO MUCH.. I DONT KNOW WHAT I WOULD HAVE DONE IF I DIDNT FIND YOUR VIDEOS. :)

[@rasmushougaard646]

These calculus videoes are top notch, better than education at universities and paid courses

[@saminm1]

I'm 16 and i understood this rule. Thank you so much. I watch your videos because they are entertaining.

[@Aukatrau]

I'd give you 5 stars but I can only give you a thumb up. Thanks for explaining stuff in such a clear manner. You are going to be the sole reason I pass AP Calculus.

[@vibha9590]

FOR THE MILLIONTH TIME, THANK YOU !!!!!!!! .

[@JNorth87]

1925 views by today, in one year, this will have 1 million + Thanks, Sal!!!!

[@sabrinakbh]

A good teacher makes a world of diference. Thank you!

[@shaktikashyap6]

No you didn't confuse us. You r the one of rare best teachers globally. And i really like ur voice and the way you talk. Thanks sir.

[@CautiousCrow]

I got a 102% in pre-cal with your help, now its summer time and learning calculus too! Wish me luck on AP Calculus the coming year hehe :)

[@DanielSmashGaming]

I tried watching a different set of lectures first and they made next to no sense, but everything you say makes absolute sense! Thank you!

[@nklamusing]

Id been having trouble with calculus and its all gone after your tutorials. :) Thanks a ton, Sal!

[@dhruvupreti5120]

10mins and a chapter worth of doubts are now cleared!

[@bothigati]

i always use your videos to prepare for tests and exams. thanks for making math so much easier

[@MarcusGray-b3f]

This review well for me learning for others is great your sessions are well timed so never to long and easy to follow. I forgot how long these calculus problems can get. If I remember correctly some problems can get extremely long.

[@omgim18]

i love you. u are so much better than my math prof who just doesnt even make sense. i think u are going to be the only reason y i pass my midterm tomro. THANKS. u are doing an amazing job. keep it up!

[@Meera781]

And helping dreams too..I am back to maths after couple of years of break and here I found my class ! God bless you Sir !

[@monday2471]

thank you so much for doing this! i can never learn properly in school because my mind wanders a lot, and if i miss even 1 thing the teacher says, i won't understand the entire lesson! but i can always replay videos and that's the best part

[@millscheeseXD]

still saving lives, i tip my hat off to you sir

[@theorist353]

Hey how's is it going pal After 7 years

[@anitapansari1]

Never ever thought I would be smiling after learning Math.... You are math super fun... Loving it and getting confident with every passing video :-)

[@JoshuaJones-te1ef]

You are a life saver. My lecture is super smart, but you seem to explain it in a more understandable way

[@pakoluevano]

dude you are the best math teacher ever man.... good job i get this stuff man thanks.!!!

[@michele7656]

2:25 "To the minuuus 8." I don't know why, but something about the way you said that was hilarious. Thank you for making these videos and being awesome.

[@omfgmedic69]

Confused me? My teacher confuses me! This is what teaching should be, taking time to explain the steps. My teacher taught us the chain rule in one class (2 hours). The next day we were given an in class assignment with the chain rule, but with fractions and rationals. In my head, I was saying ''God help me''. Teaching is an art, and thank god there are still some good teachers out there sharing their knowledge for free. Thank you.

[@musk3402]

How is your voice so soothing???

[@TheRichestCadaver]

Excellent explanation and I learned a lot, so much that I could catch a mistake, somebody also did before me. Final answer: [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] (3)[3x^-2+(5x^3-7x)^5]^2

[@MuhZubairAli]

I have no word to thank you becoz I want give you very very very very big thanks.May God Bless You....

[@jrcook-394]

This actually makes a lot more sense. My teacher taught us to go outside-in. This is a lot better in my opinion.

[@majingwei]

Khanacademy saved my life, period.

[@erin210992]

im studying egineering and i have no idea what i'd do without these vids...

[@Helllllllnaaaawww]

dude u justify the quote that says " I bunk school to study in peace". thanks man . great help

[@EytanWallace]

U have a completely different face and life than I imagined when I listened to and watched your videos!

[@the1_1one7]

It's about end of 2023 and i hope our dear teacher and all those who commented here are alive and happy 😊 sorry for my english 😅

[@topik627]

jazakum'ALLAH'UKHAYRIN! may, GOD bless you and I eveyone else watching these videos!

[@supercoupon2]

was waiting on that last set of brackets :) Great job as always.

[@mzdbnell]

This helps me more than my professor. Thankyou sooooo much.

[@MissNinita86]

I love you.....

[@djmauropicotto]

very good, i want to point out just one thing , in the last problem you need to put a parenthesis "or brackets"in [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] so that way it would be [(15x^2-7)(5)(5x^3-7x)^4-6x^-3] (3)[3x^-2+(5x^3-7x)^5]^2

[@peacefulalien2080]

You are explaining 20x better than my teacher . Keep it up good sir ! You're awesome!

[@aarya1245]

Forever grateful to Sal!

[@goofguy316]

YOU ARE A MESSIAH..... Of my marks, thank you so much!

[@serprex]

Good at explaining with a lack of assumptions, and the mouse writing is clean too

[@gocanadayayyy]

My god I feel so sorry for the people in the comments here that have teachers who don't explain it this way! My math teacher was excellent and she always made sure to go through everything step by step, even when we had two months less than everyone else to do calc (IB is hard). I'm glad these videos are here for people who aren't lucky enough to have teachers this amazing in school.

[@kimshoshi]

wow. amazing. thankyou! my $4000 tuition money for the subject would be better off with you...atleast itd pay off by me actually learning something. thankyou soo much

[@MrSamarthz]

you didn't confuse us ...you just cleared all our confusions !

[@crossfuse]

this is soooo much easier for me to understand...i havn't been getting good grades in calc and i think im finally getting caught up

[@0verlordQc]

Thanks for all your videos! Very helpful in exam period!

[@dogwithwigwamz.7320]

I appreciate the work done and time given in producing these videos but Good God - perhaps we could all chip in a few quid and enable Khan to purchase some more refined writing and video software. In other words, I suspect that many whom wish to learn Maths pause the video, in order to follow it through and reckon it in their own heads. But its almost impossible to see what is written.

[@chaim5397]

this is from 2007 he prob upgraded

[@PressStartLetsPlay]

B J is correct. The video is from 2007. Not only was the technology not great at the time, video quality was also not HD.

[@Alive4Metal]

Omg... I actually got that.... if my University professor had attempted to teach me this then there is no way in hell i would have followed so clearly.

[@TheShelbyiskool]

My savior :'). I was scared, and instead of going to church, I went to Khan Academy.

[@XJetBoomX]

Sal should make a playlist dedicated to teaching "teachers" to teach.

[@bloodybigballz]

i actually followed through the whole problem, thank you.

[@alexandrasvdavis]

Thanks for all you do Khan Academy

[@vankhun17]

Wow. Your explaination is so short and easy to understand ! thank you

[@inioluwaolaleye9434]

It's 2020 and this is still so useful, I never knew calculus was actual this easy until you explained it.

[@EmreMarinos]

fr

[@anoelst]

Khan is brilliant!

[@siriuslyD]

you're so much better than my current calculus professor, THANK YOU!

[@jhamel]

this guy is dangerously good.

[@Ureyeuh]

I want a shirt with Sal's face smiling inside of a heart.

[@samuelsrinivasvara7681]

So.. so.. so.....good one of the best e-tutors....!!!!!😀😀😊😊😊🌀

[@thebobhannah]

He does that, but in reverse order. Where the brown in the last line is the derivative of the large bracket, the pink times the green accounts for the derivative of the inner portion you mentioned: dy/dx (3x(-2)+(5x(3)-7x)(5). The light blue is the derivative of the last remaining inner portion: dy/dx (5x(3)-7x)(5). I was taught to tackle the outside first, so his method appeared a little backwards to me at first.

[@manassehleonard2879]

You do make maths easier. Thanks Khan.

[@dinamansour3469]

Thank you so much! Your way of teaching is amazing!

[@michelvellve]

Nice tutorial! It really helped me with my homework :D Thanks for sharing your knowledge xD

[@nixenberq]

Yeah man, you are awsome, thank you for your lessons !!! Thought I can't learn these things :-D, but its quite clear now, you saved me a lot of time...

[@PoncyPenguin]

I noticed you wrote a ^2 instead of a ^1, you were showing that there is a ^1 but when you copied it down in yellow you mistook it for a 2 :) Thanks for this anyway

[@urielveco]

4:20 Yay, not only have I learned something, Sal learned with me as well ^ - ^ and he's so happy about it...

[@rifathossain6140]

what a legend

[@najahdavenport8650]

Very Helpful, thankful !

[@bangbang8153]

just googled Sal and found out he has an MBA from harvard, a bachelor AND a master of science from MIT........... GOAT

[@david0aloha]

I like the videos, but I find it much easier to think about it in terms of a function of a function (of a function). eg. f(g(x)) or f(g(h(x))) For a simple one: dy/dx = d/dx f(g(x)) = f'(g(x)) * g'(x) For a more complex one: dy/dx = d/dx f(g(h(x))) = f'(g(h(x))) * g'(h(x)) * h'(x) For even more complex (like that example): dy/dx = d/dx f(x + g(h(x))) = f'(x + g(h(x))) * (dx/dx + g'(h(x)) * h'(x)) Maybe not the best notation to learn first, but makes solving ones like that last problem easier.

[@alejandroseetal2275]

Perfect example . Thanks 👍👍👍👍

[@PianoSonata]

He's Indian. Such wonderful people. Very educated.

[@Chat2Conaz]

WOOHOO! Thumbs Up! if your the 100,000 viewer! I love Khan Academy and these videos!

[@yueting0723]

thank you!! my finals on thursday this is very helpful!

[@BFrei46z]

Mine is this Thursday. How did you do?

[@Mythrunes]

Bryan Frei Rejected

[@Mythrunes]

Bryan Frei Rejected

[@likemyvibe8930]

+Mythrunes lol

[@tiffanyschwartz6339]

You are a saint.