I think I know how to differentiate it, this is what I did:

f(x)=cos^2(sinx)

f'(x)=[(2)(cos)(-sin)(sinx)](cosx)

and the answer is:

=-2cos(sinx)[sin(sinx)](cosx)

Why are there so many brackets being used in the answer? Couldn't I have went from my step 2 to:

=-2cos(sinx)sin(sinx)(cosx)?