  We study of the accuracy of the Regge behavior of the gluon distribution
function for obtain an approximation relation, which is frequently used to
extract the logarithmic slopes of the structure function from the gluon
distribution at small $x$. We show that the Regge behavior analysis results are
comparable with HERA data and also are better than other methods that expand of
the gluon density at distinct points of expansion. Also we show that for
$Q^{2}=22.4 GeV^{2}$, the $x$ dependence of the data is well described by gluon
shadowing corrections to GLR-MQ equation. The resulting analytic expression
allow us to predict the logarithmic derivative
$\frac{{\partial}F_{2}(x,Q^{2})}{{\partial}lnQ^{2}}$ and to compare the results
with H1 data and a QCD analysis fit with MRST parametrization input.
