theorem :: FDIFF_11:16

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