theorem Th6: :: FDIFF_5:6

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