Question

If f(x) = g(u) and u = u(x) then

(A) f '(x) = g '(u)
(B) f '(x) = g '(u) . u '(x)
(C) f '(x) = u '(x)

Answer 1

This is the chain rule. Do you know it?

Answer 2

To be concrete, let's say
f(x) = y = (1 + 2x)^2
let
u = 1 + 2x
y = u^2
How to get dy/dx?

Answer 3

yeah.... :)
The problem is that i dunno calculus.... its not even in my syllabus

Answer 4

Do you know how to do derivatives by the power rule?

Answer 5

Well, think of it this way:
dy/dx = dy/du times du/dx
we can *cancel* the du's

Answer 6

okay...... then

Answer 7

So for my example we do
dy/du = 2u
du/dx = 2
dy/dx = dy/du du/dx = 4u = 4(1 + 2x)
which you can check by multiplying out.

Answer 8

so is the answer (b) correct??

Answer 9

Yes

Answer 10

owhkay...thank you so much !!

Answer 11

yw