Question

What is the f'(x) of f(X)=sin^3x

Answer 1

Have you attempted this one yet ?

Answer 2

yeah

Answer 3

\[f(x) = \sin ^{3}(x)\]

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

Answer 4

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

Answer 5

that is 3u^2

Answer 6

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

Answer 7

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

Answer 8

cosx^2

Answer 9

What is the derivative of sin(x) ?

Answer 10

COS

Answer 11

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 ?