theorem :: FDIFF_11:45

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)) ) )