theorem :: FDIFF_10:20

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