  We consider the linear growth of matter perturbations in various dark energy
(DE) models. We show the existence of a constraint valid at $z=0$ between the
background and dark energy parameters and the matter perturbations growth
parameters. For $\Lambda$CDM $\gamma'_0\equiv \frac{d\gamma}{dz}_0$ lies in a
very narrow interval $-0.0195 \le \gamma'_0 \le -0.0157$ for $0.2 \le
\Omega_{m,0}\le 0.35$. Models with a constant equation of state inside General
Relativity (GR) are characterized by a quasi-constant $\gamma'_0$, for
$\Omega_{m,0}=0.3$ for example we have $\gamma'_0\approx -0.02$ while
$\gamma_0$ can have a nonnegligible variation. A smoothly varying equation of
state inside GR does not produce either $|\gamma'_0|>0.02$. A measurement of
$\gamma(z)$ on small redshifts could help discriminate between various DE
models even if their $\gamma_0$ is close, a possibility interesting for DE
models outside GR for which a significant $\gamma'_0$ can be obtained.
