## Why partial derivatives in continuity equation?

Why is partial derivative with respect to time used in the continuity equation,
$$\frac{\partial \rho}{\partial t} = - \nabla \vec{j}$$
If this equation is really derived from the equation,
$$\frac{dq}{dt} = - \int\int \vec{j} \cdot d\vec{a}$$
Then should it be a total derivative with respect to time?
 Partial derivative is used because the charge density may also vary with distance.