Assume that
f(0) = 2 and f '(0) = 3.
Calculate the derivative of the following function at
x = 0...... (f(x))^3

Question

Assume that 
f(0) = 2 and f '(0) = 3.
 Calculate the derivative of the following function at 
x = 0...... (f(x))^3

myininaya · Answer

of the following function?

myininaya · Answer

because if we are just computing the derivative of the function f at x=0 then that is already given

anonymous · Answer

Sorry! Forgot the final bit

myininaya · Answer

USe the chain rule there

myininaya · Answer

to differentiate (f(x))^3

anonymous · Answer

That's where I'm at a loss. I get 3f'(x) and I thought that'd just be 9 but it's not...

myininaya · Answer

ok well do you the chain rule is this:
$$[f(g(x))]'=g'(x) \cdot f'(g(x))$$

anonymous · Answer

oh nvm I forgot I was using an exponent. Time to redo everything!

anonymous · Answer

Thanks though

myininaya · Answer

let me change those function names up a little 
$$[g(f(x))]'=f'(x) \cdot g'(f(x))$$

myininaya · Answer

using this bottom thing I said here g=x^3
do you know how to different g?

anonymous · Answer

Indeed I do. I just realized I did the wrong thing and didn't use the exponent rule

myininaya · Answer

$$[g(f(x))]'=f'(x) \cdot g'(f(x)) =f'(x) \cdot 3(f(x))^2$$

oh okay! 
so you got this then?

anonymous · Answer

Yes! Thanks a lot! Sometimes it just takes a fresh brain to help see what I did wrong.