theorem :: FDIFF_11:48

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)) + ((2 * (sec . x)) / (1 + (x ^2))) ) )