theorem Th6: :: FDIFF_9:6

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