theorem :: SIN_COS9:117

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