Question

What is the derivative of `f(x)=log_2(cos(x))` ?

Answer 1

`-tan(x)/ln(2)`

Explanation:

`f(x)=log_2(cos(x))=ln(cos(x))/ln(2)`

`1/ln(2)` is just a constant and can be ignored.

`(ln(u))'=(u')/u`

`u=cos(x), u'=-sin(x)`

`f'(x)=1/ln(2)*(-sin(x))/cos(x)=-tan(x)/ln(2)`