Answer
See explanation
Work Step by Step
Having a differentiable function $f(x, y)$ of two variables, we can define the partial derivatives of $f$ with respect to $x$ and $y$ as $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$. A derivative of $f$ should contain these two entities. This is why the gradient of $f$ is a great candidate for being called a "derivative" of a two-variable function, as it has the two partial derivatives within its expression: \[ \nabla f = \frac{\partial f}{\partial x} \mathbf{i} + \frac{\partial f}{\partial y} \mathbf{j} \]
