theorem Th7: :: FDIFF_8:7

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