let th be real number ; :: thesis: ( exp_R is_differentiable_on REAL & diff exp_R ,th = exp_R . th )
A1: ( [#] REAL is open Subset of REAL & REAL c= dom exp_R ) by FUNCT_2:def 1;
A2: for r being Real st r in REAL holds
exp_R is_differentiable_in r by Th70;
thus ( exp_R is_differentiable_on REAL & diff exp_R ,th = exp_R . th ) by A1, A2, Th70, FDIFF_1:16; :: thesis: verum