## anonymous 3 years ago What is the f'(x) of f(X)=sin^3x

• This Question is Open
1. anonymous

Have you attempted this one yet ?

2. anonymous

yeah

3. anonymous

$f(x) = \sin ^{3}(x)$ Did I write this down correctly? If so, try substitution. For example, let u = sin(x) and then take the derivative of u^3

4. anonymous

I got f'(X) is 9x^2cosx^2

5. anonymous

that is 3u^2

6. anonymous

3u^2 du/dx, yes. Now what is du/dx if u = sin x?

7. anonymous

In other words, what is u' if u = sin x

8. anonymous

cosx^2

9. anonymous

What is the derivative of sin(x) ?

10. anonymous

COS

11. anonymous

Great, so du/dx = cos x So we have 3u^2 * cos x Substitute u = sin(x) back in and what do we end up with ?

12. anonymous

|dw:1357249368629:dw|