theorem :: FDIFF_8:30

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