theorem :: FDIFF_9:17

for Z being open Subset of REAL st Z c= dom (exp_R * cosec) holds
( exp_R * cosec is_differentiable_on Z & ( for x being Real st x in Z holds
((exp_R * cosec) `| Z) . x = - (((exp_R . (cosec . x)) * (cos . x)) / ((sin . x) ^2)) ) )