theorem :: FDIFF_4:46

for Z being open Subset of REAL st Z c= dom (((- (id Z)) (#) cos) + sin) holds
( ((- (id Z)) (#) cos) + sin is_differentiable_on Z & ( for x being Real st x in Z holds
((((- (id Z)) (#) cos) + sin) `| Z) . x = x * (sin . x) ) )