Define what it means for a function $f: \mathbf{R}^{2} \rightarrow \mathbf{R}$ to be differentiable at a point $(a, b)$. If the partial derivatives $\partial f / \partial x$ and $\partial f / \partial y$ are defined and continuous on a neighbourhood of $(a, b)$, show that $f$ is differentiable at $(a, b)$.