theorem :: FDIFF_11:3

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