Example 2.2.2: Divergence of a vector field

Each component is differentiated with respect to its own coordinate, as in (2.2.6):

The result is a scalar field. It is non-negative everywhere: every point off the plane $z=0$ is a source of this field, and the plane $z=0$ is neither a source nor a sink. Note that the $z$-component, although it depends on $x$ and $y$, contributes nothing, because it does not change along its own direction.