Question

How do you find the derivative of `Cos^4(2x)`?

Answer 1

Use the chain rule twice.

Explanation:

Recall that we use the notation `cos^4 (u)` to mean `(cos(u))^4`

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

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

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

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