  We present forecasts on the capability of future wide-area high-sensitivity
X-ray surveys of galaxy clusters to yield constraints on the parameters
defining the Dark Energy (DE) equation of state (EoS). Our analysis is carried
out for future X-ray surveys which have enough sensitivity to provide accurate
measurements of X-ray mass proxies and Fe-line based redshifts for about 2x10^4
clusters. We base our analysis on the Fisher Matrix formalism, by combining
information on the cluster number counts and power spectrum, also including,
for the first time in the analysis of the large scale cluster distribution, the
effect of linear redshift-space distortions (RSDs). This study is performed
with the main purpose of dissecting the cosmological information provided by
geometrical and growth tests, which are both included in the analysis of number
counts and clustering of galaxy clusters. We compare cosmological constraints
obtained by assuming different levels of prior knowledge of the parameters
which define the observable-mass X-ray relation. This comparison further
demonstrates the fundamental importance of having a well calibrated
observable-mass relation and, most importantly, its redshift evolution. Such a
calibration can be achieved only by having at least $\sim 10^3$ net photon
counts for each cluster included in the survey. We show that RSDs in the power
spectrum analysis carry important cosmological information also when traced
with galaxy clusters and the DE FoM increases by a factor of 8. Besides
confirming the potential that large cluster surveys have in constraining the
nature of DE, our analysis emphasizes that a full exploitation of the
cosmological information carried by such surveys requires not only a large
statistic but also a robust measurement of the mass proxies and redshifts for a
significant fraction of the cluster sample, derived from the same X-ray survey
data.
