  In this paper, we aim to investigate the optimal decay rate for the higher
order spatial derivative of global solution to the full compressible
Navier-Stokes (CNS) equations with potential force in $\mathbb{R}^3$. We
establish the optimal decay rate of the solution itself and its spatial
derivatives (including the highest order spatial derivative) for global small
solution of the full CNS equations with potential force. With the presence of
potential force in the considered full CNS equations, the difficulty in the
analysis comes from the appearance of non-trivial ststionary solutions. These
decay rates are really optimal in the sense that it coincides with the rate of
the solution of the linerized system. In addition, the proof is accomplished by
virtue of time weighted energy estimate, spectral analysis, and high-low
frequency decomposition.
