theorem Th40: :: INTEGR13:40

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