In a particular reference frame with coordinates $x^\mu$, we can define a current density 4-vector $J^\mu=(c\rho,\vec{J})$ where $\rho$ is the charge density and $\vec{J}$ is the current density.

The continuity equation in this frame is then $$\frac{\partial J^\mu}{\partial x^\mu}=0.$$

How can it be shown that this equation holds in a Lorentz boosted frame with coordinates $x'^\mu=\Lambda^\mu\_\nu x ^\nu$,
i.e. $$\frac{\partial J'^\mu}{\partial x'^\mu}=0$$ is true?