theorem :: FDIFF_9:16

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 . (sec . x)) * (sin . x)) / ((cos . x) ^2) ) )