theorem :: FDIFF_11:32

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