theorem Th17: :: FDIFF_7:17

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