Question concerning chain rule for multivariable functions

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I'm working with a two 2-variable-functions that depend on $x$ (called $R$ and $r$) and I'm trying to figure out what $\frac{\partial}{\partial x}$ is. My book gives the following answer: $\frac{\partial}{\partial x}=\frac{\partial}{\partial R}\frac{\partial R}{\partial x}+ \frac{\partial}{\partial r}{\frac{\partial r}{\partial x}}$. I know how the chain rule works, but I would like to see a proof concerning this relation.