theorem :: FDIFF_8:28

for a, b being Real
for Z being open Subset of REAL
for f being PartFunc of REAL,REAL st Z c= dom (f (#) tan) & ( for x being Real st x in Z holds
f . x = (a * x) + b ) holds
( f (#) tan is_differentiable_on Z & ( for x being Real st x in Z holds
((f (#) tan) `| Z) . x = ((a * (sin . x)) / (cos . x)) + (((a * x) + b) / ((cos . x) ^2)) ) )