theorem Th7: :: FDIFF_6:7

for Z being open Subset of REAL
for f1, f2 being PartFunc of REAL,REAL st Z c= dom (f1 / (f2 + f1)) & f1 = #Z 2 & ( for x being Real st x in Z holds
( f2 . x = 1 & x <> 0 ) ) holds
( f1 / (f2 + f1) is_differentiable_on Z & ( for x being Real st x in Z holds
((f1 / (f2 + f1)) `| Z) . x = (2 * x) / ((1 + (x ^2)) ^2) ) )