theorem :: FDIFF_8:8

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