  We apply the Lagrangian perturbation theory with time-dependent growth
functions at second and third order of perturbation with the aim to model the
effect of dynamical dark energy on redshift-space distortions. Our fiducial
galaxy redshift surveys are modeled after the upcoming SKA and DESI redshift
surveys. We include PLANCK CMB priors and the 20\% uncertainty on the linear
bias parameter, incorporating the unknown instrumentation noise. After the
marginalizing, our results show that the constraints on the density parameter
could potentially get better than $\sim$1\%, while the constraints on $w_0$ and
$w_{\rm a}$ could be better than $\sim 5\%$ and $\sim 60\%$ respectively,
consistent with works done before. However, the inclusion of time-dependent
growth functions would alter the nonlinear power spectrum by as much as
$\sim$10\%. The inclusion of the time-dependent growth functions become crucial
as the precision gets better.
