theorem :: FDIFF_5:15

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