theorem :: SIN_COS9:90

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