2. Given a function $\displaystyle f : \mathbb{R}^3 \to \mathbb{R}$, $\displaystyle f \in C^{1}$, the gradient of that function is a vector whose components in Cartesian coordinates are $\displaystyle \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)$.