theorem :: FDIFF_7:43

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