What is meant by rate of change with respect to volume?

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In physics we often come across $$\rho=\dfrac{dq}{dV}$$

Does it mean:

$(i)$ $\displaystyle \lim_{\Delta V \to 0} \dfrac{\Delta q}{\Delta V}$

OR

$(ii)$ $\dfrac{\partial}{\partial z} \left( \dfrac{\partial}{\partial y} \left( \dfrac{\partial q}{\partial x} \right) \right)$

What does the first one mean?

The second one is a mixed partial derivative. Can it be found if $q, \dfrac{\partial q}{\partial x}, \dfrac{\partial}{\partial y} \left( \dfrac{\partial q}{\partial x} \right)$ are differentiable?