Question

What is the derivative of `ln(cos 2x)`?

Answer 1

I found:`f'(x)=-2sin(2x)/cos(2x)=-2tan(2x)`

Explanation:

Here I would use the Chain Rule applied to your function:
`f(x)=ln(cos(2x))`
deriving `ln` as it is, multiplying by the derivative of `cos` as it is (red) and finally multiplying by the derivative of `2x` (blue):
`f'(x)=1/cos(2x)*color(red)(-sin(2x))*color(blue)(2)=-2sin(2x)/cos(2x)=-2tan(2x)`