Question

What is the derivative of `f(x)=log(sin^2(x))`?

Answer 1

`f' (x)=2*log e*cot x`

Explanation:

From the given `f(x) = log (sin^2 x)`

The formula for finding the derivative of logarithm

`d/dx(log_a u)=1/u*log_a e*d/dx(u)`

`d/dx(f(x))=d/dx(log (sin^2 x))=1/sin^2 x*log e*d/dx(sin^2 x)`

`d/dx(f(x))=d/dx(log (sin^2 x))=1/sin^2 x*log e*2*sin x*cos x`

`d/dx(f(x))=2*log e*cot x`

God bless....I hope the explanation is useful.