theorem :: FDIFF_11:58

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