When is time a degree of freedom? I was doing a problem, and made a mistake and said that
$\vec{\nabla} \cdot \vec{F}(\vec{r},t) = \frac{\partial F(\vec{r},t)}{\partial x} + \frac{\partial F(\vec{r},t)}{\partial y} + \frac{\partial F(\vec{r},t)}{\partial z} + \frac{\partial F(\vec{r},t)}{\partial t}$
This, I discovered, is wrong, as the partial time derivative should be left out. My question pertains to the reason for this. When do we treat time as a degree of freedom that should be included in the divergence (or curl or gradient (in the case of a scalar function))?