theorem :: FDIFF_11:34

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 . x) * (arccot . x)) / ((cos . x) ^2)) - (1 / ((cos . x) * (1 + (x ^2)))) ) )