theorem :: FDIFF_5:16

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