theorem Th5: :: FDIFF_5:5

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