theorem :: FDIFF_11:57

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 = 0 ) )