theorem :: FDIFF_9:12

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