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