theorem :: FDIFF_4:21

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)) & f2 = #Z 3 & ( for x being Real st x in Z holds
( f1 . x = a & (f1 + 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 = (3 * (x |^ 2)) / (a + (x |^ 3)) ) )