  We present a set of independent formulae to extract the gluon distribution
and singlet structure function from its derivatives with respect to $lnQ^{2}$
in the next- to- leading order of perturbation theory at low-$x$ based on a
hard pomeron exchange. In this approach, both singlet quarks and gluons have
the same high-energy behavior at small $x$. This approach needs the QCD input
parameterizations for a independent DGLAP evolutions that we calculated
numerically and compared with MRST, GRV and DL model- the Pomeron has a hard
nature. Its evolution gives a good fit to the experimental data. The obtained
values are in the range
$10^{-4}\hspace{0.1cm}{\leq}\hspace{0.1cm}x\hspace{0.1cm}{\leq}10^{-2}$ at
$Q^{2}=20 \hspace{0.1cm}GeV^{2}$.
