theorem :: FDIFF_11:46

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