theorem :: FDIFF_9:24

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