theorem :: FDIFF_11:35

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