theorem Th106: :: SIN_COS9:106

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