theorem :: FDIFF_11:17

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