theorem :: FDIFF_11:15

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