theorem :: FDIFF_7:41

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