theorem :: FDIFF_5:8

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