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

1. anonymous

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.

2. rational

differentiate using chain rule

3. rational

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

4. anonymous

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.

5. anonymous

6*3*-3^2?

6. rational

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

7. anonymous

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

8. rational

variables are just dummy

9. rational

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

10. anonymous

XD

11. anonymous

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

12. rational

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

13. rational

plugin $$x=5$$

14. rational

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