Question

How do you find the derivative of `cos^3(2x)`?

Answer 1

Use the chain rule twice.

Explanation:

First recall that `cos^3(2x) = (cos(2x))^3`

So,

`d/dx(cos^3(2x)) = 3cos^2(2x) d/dx(cos(2x))`

`= 3cos^2(2x) (-sin(2x)) d/dx(2x)`

`= 3cos^2(2x) (-sin(2x)) (2)`

`= -6cos^2(2x) sin(2x)`