theorem :: FDIFF_10:41

for Z being open Subset of REAL st Z c= dom ((tan - cot) / exp_R) holds
( (tan - cot) / exp_R is_differentiable_on Z & ( for x being Real st x in Z holds
(((tan - cot) / exp_R) `| Z) . x = ((((1 / ((cos . x) ^2)) + (1 / ((sin . x) ^2))) - (tan . x)) + (cot . x)) / (exp_R . x) ) )