theorem :: FDIFF_8:29

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