theorem :: SIN_COS9:118

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