theorem :: FDIFF_11:72

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