theorem :: FDIFF_11:12

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