= Solution
For a <canonical ensemble>, $F=-k_BT\ln Z$ and $p=-(\partial F/\partial V)_{T,N}=k_BT(\partial_V\ln Z)_{T,N}$. The kinetic and <factorial> factors do not depend on $V$, so differentiating only the volume-dependent terms gives
$$
p=k_BT\left[\frac{N}{V-Nb}-\frac{aN^2}{k_BTV^2}\right].
$$
Thus the <equation of state> is
$$
\boxed{\left(p+\frac{aN^2}{V^2}\right)(V-Nb)=Nk_BT},
\qquad V>Nb.
$$
The excluded-volume correction raises <pressure> relative to the same gas without that correction; the attractive mean-field term lowers it. No <Stirling formula> is required for this <derivative>.
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