theorem :: FDIFF_5:14

for Z being open Subset of REAL st not 0 in Z & Z c= dom (((id Z) ^) (#) sin) holds
( ((id Z) ^) (#) sin is_differentiable_on Z & ( for x being Real st x in Z holds
((((id Z) ^) (#) sin) `| Z) . x = ((1 / x) * (cos . x)) - ((1 / (x ^2)) * (sin . x)) ) )