theorem :: FDIFF_6:47

for Z being open Subset of REAL st Z c= dom (((1 / 3) (#) ((#Z 3) * cos)) - cos) holds
( ((1 / 3) (#) ((#Z 3) * cos)) - cos is_differentiable_on Z & ( for x being Real st x in Z holds
((((1 / 3) (#) ((#Z 3) * cos)) - cos) `| Z) . x = (sin . x) |^ 3 ) )