theorem :: FDIFF_9:43

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