theorem Th24: :: FDIFF_4:24

for a, b 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 = x - a & f1 . x > 0 & f2 . x = x - b & 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 = (a - b) / ((x - a) * (x - b)) ) )