theorem :: SIN_COS9:94

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