Question

How do you find the derivative of `log(sin^2(x))`?

Answer 1

`d/(dx)log(sin^2x)=2cotx`

Explanation:

To differentiate `f(x)=log(sin^2x)`m we use chain rule i.e.

first differentiating `log(sin^2x)` w.r.t. `sin^2x` and then

differentiating `sin^2x` w.r.t. `sinx` and finally

differentiating `sinx` w.r.t. `x`.

Thus `(df)/(dx)=(1/sin^2x)* (2sinx)* (cosx)=(2cosx)/sinx=2cotx`