Question

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

Answer 1

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

Explanation:

One way would be to use the Chain Rule, deriving `ln` first (red) and then in sequence multiply by the derivative of `cos` (blue) and `2x` (black) to get:
`f'(x)=color(red)(1/cos(2x))*color(blue)(-sin(2x))*2=`
`=-2(sin(2x))/(cos(2x))=-2tan(2x)`