theorem :: FDIFF_11:61

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