Chain rule | Derivative rules | AP Calculus AB | Khan Academy

The chain rule states that the derivative of f(g(x)) is f'(g(x))_g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x_) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x_. Using the chain rule and the derivatives of sin(x) and x_, we can then find the derivative of sin(x_). Created by Sal Khan.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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[Fish-vsjf]

This left me far more confused than when I started

[Eeeurrrrrr]

I praise thy holy salaman kotal khan for his great work in the field of mathamatics. Without his holy butttery voice, I would be but a mere padwan of what I am today

[EastSideGameGuy]

I sometimes come here to listen to his voice ._. it's soothing makes math Beautiful

[lidestudios]

I only watched this to review, I already know how the chain rule works, but the way he explained it makes it look more complicated than “derivative of outside when x= inside function, times derivative of the inside”

[Jorge-]

Everyone in the comments talking about math stuff while I'm over here trying to count how many times he said respectively. I'm just over here thinking how much respect is in this video.

[chawza]

oh my god! my teacher taught me this but never mentioned it's called chain rule. I blindly use this method without knowing what it is for!

[chrisfreilich]

Still trying to figure out EXACTLY what 'with respect to' means. People always seem to gloss over it or talk around it.

[abhilashmishra]

this video just saved me from failing in Physics. Thanks a lot Sal sir

[p.c]

What is the problem with some college/university teachers. is it laziness? I guess it is pride - it seems they dont want subjects to appear simple, too simple for students to suddenly catch what they spent many years to train for. It is not only right, but an honest thing to "call a spade a spade." Thanks KA!

[BoZhaoengineering]

This planet needs you! Thank you for the learning videos!

[rajingajadhar]

Found this channel in grade 12, and I'm coming back to it now in my final year (hopefully) of uni.

[Jcava]

sorry, i feel like you shouldn't have used sin x, and instead just a simpler function. ive learned and understood the chain rule before and came here for a refresher and this didnt help :(

[ernstboyd]

in the case of a linear function (where the function is just multiplying x by a constant)
the derivative is just the product of the two derivatives.
if f(x) = 5x and g(x) = 10x. then. g(f(x)) = 50x. and (50x)' =. f'(x) * g'(x) = 50
if the outer function is not linear like g(x) = x^2 then the slope changes depending on the
input it gets from the inner function f this is why the slope of the g(x) should be evaluated at the
same value as it gets from f(x)
in other words. (g(f(x)))' = f'(x) *. g'(f(x))

[OppenheimerUpandcoming]

OMG I FINALLY UNDERSTOOD THIS THING THANK U SO MUCH

[Syntaxxed]

all those hours in school vs a 5 min yt video... it keeps happening but I keep being amazed

[Yues]

wow super thanks mr.Khan kumar, now i really understand with this thing called chain rule how it work, but still cant visualized it but thanks i clearly know how it works now

[oferzilberman]

I didn't quite understand what does it mean "With respect to something", And quora and google didn't really help, Can someone help me on this?

Edit: I figured it out and it turns out it just means it's the x axis but now it can be substitued as other variables like t, So when it's "with respect to something" it means that the y equation is using that variable as the x

[SUMANKARANTH-uy]

The power/chain rule is the saviour of math

[konvictz]

Hi Sal, love your videos. Just need to update it to 1080p, will look sharper on bigger screens.

[qualquan]

The U substitution of inner x terms is simpler
2nd step is finding dU by differentiating U = dU/dx to express everything in x terms
So 2 successive differentiations. "Outer and "inner""
Final result expressed as a differential coeff (DC) as a rule