Derive: (I'm lost on this one, I'm not sure which one is f(x) and which one is g(x). We are suppose to apply the chain rule here: f'(g(x)) g(x).

w= 100e^-x^2

Question

Derive: (I'm lost on this one, I'm not sure which one is f(x) and which one is g(x). We are suppose to apply the chain rule here: f'(g(x)) g(x). 

w= 100e^-x^2

precal · Answer

I would just take the derivative of both sides
so it becomes
w ' =

precal · Answer

Let me type the equation first to verify

precal · Answer

$$w=100e ^{-x ^{2}}$$

precal · Answer

is this correct before we do the chain rule

issy14 · Answer

yes correct

precal · Answer

the derivative of e^u    is u ' (e^u)

precal · Answer

wait your notation is throwing me off, let me apply chain rule and then explain it

issy14 · Answer

ok

precal · Answer

u=-x^2
u ' = -2x

precal · Answer

$$w ' =-2x(100)e ^{-x^2}$$

precal · Answer

$$w ' =-200e ^{-x^2}$$

precal · Answer

ok that is your answer
you need to memorize
d/dx of e^u= u ' (e^u)
this way your chain rule is built in

precal · Answer

hope that helps you

issy14 · Answer

ok, may I ask you another question, Is that how I should approach chain rule problems?

precal · Answer

inner function by the way is u so that is your g(x) and the outer function is f(x) in this case 100e^x 
I find it easier to say who is the inner function, call it u and then take the derivative of u and call it u '

issy14 · Answer

I always try to separate it as well, this one just threw me off completely thank you.

issy14 · Answer

I'm taking calc I over the summer and its not an easy task