theorem :: FDIFF_7:4

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