theorem :: FDIFF_11:1

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