theorem :: SIN_COS9:121

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