What is the derivative of the given function f(x)?

[TG3]

Homework Statement

Differentiate sin x - 1/3 sin^3 (x) + 7

The attempt at a solution

sin x becomes cos x, and 7 becomes 0.
Using the product rule on (1/3) sin^3 (x) + 7 I get:
(0) sin^3 x + (1/3) [derivative of sin^3 (x)]

Getting the derivative of sin^3(x) is the tricky part I'm struggling with.
I would have thought it would be 3 sin^2 (x) times cos^3(x); but I know this is wrong.

 

[tnutty]

f(x) = sin x - 1/3 sin^3 (x) + 7

f '(x) = cos(x) - 1/3 * 3(sin(x))^2 * cos(x) + 0
= cos(x) - sin(x)^2 * cos(x)