theorem :: FDIFF_11:42

for Z being open Subset of REAL st 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 = (- ((sin . x) * ((arctan . x) - (arccot . x)))) + ((2 * (cos . x)) / (1 + (x ^2))) ) )