theorem Th87: :: SIN_COS9:87

for r, s being Real
for Z being open Subset of REAL
for f being PartFunc of REAL,REAL st Z c= dom (arctan * f) & ( for x being Real st x in Z holds
( f . x = (r * x) + s & f . x > - 1 & f . x < 1 ) ) holds
( arctan * f is_differentiable_on Z & ( for x being Real st x in Z holds
((arctan * f) `| Z) . x = r / (1 + (((r * x) + s) ^2)) ) )