let th be real number ; :: thesis: ( cos is_differentiable_on REAL & diff cos ,th = - (sin . th) )
A1: ( [#] REAL is open Subset of REAL & REAL c= dom cos ) by FUNCT_2:def 1;
for r being Real st r in REAL holds
cos is_differentiable_in r by Th68;
hence ( cos is_differentiable_on REAL & diff cos ,th = - (sin . th) ) by A1, Th68, FDIFF_1:16; :: thesis: verum