theorem Th44: :: INTEGR13:44

for Z being open Subset of REAL st Z c= dom ((#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)) ) )