theorem Th11: :: FDIFF_6:11

for a being Real
for Z being open Subset of REAL
for f being PartFunc of REAL,REAL st Z c= dom (exp_R * f) & ( for x being Real st x in Z holds
f . x = x * (log (number_e,a)) ) & a > 0 holds
( exp_R * f is_differentiable_on Z & ( for x being Real st x in Z holds
((exp_R * f) `| Z) . x = (a #R x) * (log (number_e,a)) ) )