theorem :: FDIFF_4:22

for a being Real
for Z being open Subset of REAL
for f1, f2 being PartFunc of REAL,REAL st Z c= dom (ln * (f1 / f2)) & ( for x being Real st x in Z holds
( f1 . x = a + x & f1 . x > 0 & f2 . x = a - x & f2 . x > 0 ) ) holds
( ln * (f1 / f2) is_differentiable_on Z & ( for x being Real st x in Z holds
((ln * (f1 / f2)) `| Z) . x = (2 * a) / ((a ^2) - (x ^2)) ) )