theorem :: FDIFF_11:59

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 = 0 ) )