theorem :: FDIFF_8:31

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