theorem :: SIN_COS9:129

for Z being open Subset of REAL st not 0 in Z & 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)))) ) )