theorem :: SIN_COS9:89

for Z being open Subset of REAL st Z c= dom (ln * arctan) & Z c= ].(- 1),1.[ & ( for x being Real st x in Z holds
arctan . x > 0 ) holds
( ln * arctan is_differentiable_on Z & ( for x being Real st x in Z holds
((ln * arctan) `| Z) . x = 1 / ((1 + (x ^2)) * (arctan . x)) ) )