theorem Th91: :: SIN_COS9:91

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