theorem :: FDIFF_11:29

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 = ((arctan . x) / ((cos . x) ^2)) + ((tan . x) / (1 + (x ^2))) ) )