theorem :: FDIFF_10:18

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