  In this paper, we establish derivative estimates for the Vlasov-Poisson
system with screening interactions around Penrose-stable equilibria on the
phase space $\mathbb{R}^d_x\times \mathbb{R}_v^d$, with dimension $d\ge 3$. In
particular, we establish the optimal decay estimates for higher derivatives of
the density of the perturbed system, precisely like the free transport, up to a
log correction in time. This extends the recent work \cite{T-R-HK} by Han-Kwan,
Nguyen and Rousset to higher derivatives of the density. The proof makes use of
several key observations from \cite{T-R-HK} on the structure of the forcing
term in the linear problem, with induction arguments to classify all the terms
appearing in the derivative estimates.
