Question

What is the derivative of `f(x)=cos^4(2x)`?

Answer 1

`-8cos^3(2x)sin(2x)`

Explanation:

`f(x) = (cos(2x))^4`

`f'(x) = 4(cos(2x))^3 d/dx(cos(2x))` (chain rule)

`= 4(cos(2x))^3 (-sin(2x) d/dx(2x))`

`= 4(cos(2x))^3 (-sin(2x) (2))`

`= -8cos^3(2x)sin(2x)`