theorem :: FDIFF_7:9

for Z being open Subset of REAL st Z c= dom (ln * arccos) & Z c= ].(- 1),1.[ & ( for x being Real st x in Z holds
arccos . x > 0 ) holds
( ln * arccos is_differentiable_on Z & ( for x being Real st x in Z holds
((ln * arccos) `| Z) . x = - (1 / ((sqrt (1 - (x ^2))) * (arccos . x))) ) )