theorem :: SIN_COS9:128

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