theorem :: FDIFF_9:42

for Z being open Subset of REAL st Z c= dom (tan (#) sec) holds
( tan (#) sec is_differentiable_on Z & ( for x being Real st x in Z holds
((tan (#) sec) `| Z) . x = ((1 / ((cos . x) ^2)) / (cos . x)) + (((tan . x) * (sin . x)) / ((cos . x) ^2)) ) )