theorem :: FDIFF_11:44

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