theorem :: FDIFF_9:39

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