theorem Th7: :: INTEGR13:7

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