theorem Th14: :: FDIFF_6:14

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 ) holds
( exp_R * f is_differentiable_on Z & ( for x being Real st x in Z holds
((exp_R * f) `| Z) . x = - (exp_R (- x)) ) )