Divergence Operator is Invariant under Coordinate Transformation

Theorem
Let $R$ be a region of space in which there exists an vector field $\mathbf V$.

Let $\nabla \cdot \mathbf V$ denote the divergence of $\mathbf V$.

Then $\nabla \cdot \mathbf V$ is invariant under a change of coordinate system on $R$.

Proof
The result follows directly from the physical interpretation of the divergence operator.