theorem :: FDIFF_11:30

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