A simple derivative that I'm messing up on

[lase]

Homework Statement

Find f'(x) for f(x) = sin x + 2 cos^3 x

Homework Equations

Other than basic derivative properties and formulas, no.

The Attempt at a Solution

f'(x) = sin x + 2cos^3 x
= cos x - 6sin^2 x

The book says the answer is f'(x) = cos x - 6cos^2 x sin x however I don't understand where the sin x comes from... any help?

 

[SammyS]

Do you know the chain rule?

 

[lase]

Yeah, d/dx[f(g(x))] = f'(g(x))g'(x). My bad, now I got the correct answer of f'(x) = cos x - 6cos^2 x sin x.. I think I used the power rule on 2cos^3 x by mistake before.