theorem :: FDIFF_10:33

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