Question

How do you differentiate `log(sin^2(x))`?

Answer 1

`2cot(x)`

Explanation:

This answer assumes that `log(x)=log_e(x)`, the natural logarithm.

First use the rule `log(a^b)=blog(a)`:

`y=log(sin^2(x))=2log(sin(x))`

From here, we need to know that `d/dxlog(x)=1/x`. Through the chain rule, `d/dxlog(f(x))=1/f(x)*f'(x)`.

Then:

`dy/dx=2(1/sin(x))(d/dxsin(x))=2/sin(x)(cos(x))=2cot(x)`