theorem :: FDIFF_11:9

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