theorem Th49: :: FDIFF_4:49

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