theorem Th16: :: FDIFF_7:16

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