  Let $Q$ be a finite acyclic valued quiver. We give the cluster multiplication
formulas in the quantum cluster algebra of $Q$ with arbitrary coefficients, by
applying certain quotients of derived Hall subalgebras of $Q$. These formulas
can be viewed as the quantum version of the cluster multiplication theorem in
the classical cluster algebra proved by Caldero-Keller for finite type, Hubery
for affine type and Xiao-Xu for acyclic quivers.
