theorem :: FDIFF_4:38

for a, b being Real
for Z being open Subset of REAL
for f being PartFunc of REAL,REAL st Z c= dom (cos * f) & ( for x being Real st x in Z holds
f . x = (a * x) + b ) holds
( cos * f is_differentiable_on Z & ( for x being Real st x in Z holds
((cos * f) `| Z) . x = - (a * (sin . ((a * x) + b))) ) )