Basic calc question. I am given the derivative and the value of y at a given x value, can i find this?

Question

anonymous · Answer

I know g(5)=-3 and g(5)'=6. I am asked to find the derivative of f(5).
I am told f(x)=[g(x)]^3 . Is this capable of being solved, and if so how.

rational · Answer

differentiate using chain rule

rational · Answer

f(x) = [g(x)]^3

f'(x) = ?

anonymous · Answer

I guessed that but what is the derivative of a floating exponent.
Im sorry if im typing slowly for some reason this site is killing my computer.

anonymous · Answer

6*3*-3^2?

rational · Answer

use this
$$\frac{d}{dx}x^n ~=~n*x^{n-1}$$

anonymous · Answer

Yeah thats like the first rule of differntation you learn, but does it still appy without a varible x?

rational · Answer

variables are just dummy

rational · Answer

$$\large \frac{d}{d\clubsuit} \clubsuit^n ~= ~n*\clubsuit^{n-1} $$

anonymous · Answer

XD

anonymous · Answer

S0 6*3*(-3)^2 would fit that or not?

rational · Answer

$$ f(x) = [g(x)]^3$$

$$f'(x) = 3*[g(x)]^{3-1} * \color{red}{g'(x)}$$

rational · Answer

plugin $x=5$

rational · Answer

6*3*(-3)^2  looks good!