Answer
$f'(x)=\dfrac{\cos{x}\sin{x}}{|\sin{x}|};x\ne n\pi$ for $n=0, 1, 2, 3, ...$
Work Step by Step
Using the Chain Rule:
$u=\sin{x}$; $u'=\cos{x}$ $f'(x)=u'\dfrac{u}{|u|}$
$=\dfrac{\cos{x}\sin{x}}{|\sin{x}|};x\ne n\pi$ for $n=0, 1, 2, 3, ...$
