theorem Th54: :: INTEGR13:54

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