theorem :: FDIFF_11:23

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 . (arctan . x)) / (((sin . (arctan . x)) ^2) * (1 + (x ^2)))) ) )