theorem :: FDIFF_11:47

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