theorem :: FDIFF_11:60

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