theorem Th10: :: FDIFF_7:10

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