theorem Th88: :: SIN_COS9:88

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