theorem :: FDIFF_4:48

for Z being open Subset of REAL st Z c= dom (2 (#) ((#R (1 / 2)) * sin)) & ( for x being Real st x in Z holds
sin . x > 0 ) holds
( 2 (#) ((#R (1 / 2)) * sin) is_differentiable_on Z & ( for x being Real st x in Z holds
((2 (#) ((#R (1 / 2)) * sin)) `| Z) . x = (cos . x) * ((sin . x) #R (- (1 / 2))) ) )