Question

differentiate f(x)=ln (sinxcosx)

Answer 1

all you need to do is use log properties...
\[\ln(\sin(x)\cos(x))= \ln(\sin(x)) + \ln(\cos(x))=f(x)\]

Answer 2

\[f'(x) = \frac{\cos(x)}{\sin(x)}-\frac{\sin(x)}{\cos(x)}\]

Answer 3

\[f'(x) = \cot(x) - \tan(x)\]

Answer 4

or
\[= \frac{ \cos^2{(x)}-\sin^2{(x)} }{ \sin(x)\cos(x) }\]