theorem :: FDIFF_11:40

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