One would need to specify it a lot more precisely to elevate either the 1D example you gave, or the 3D one I'll give, to the status of a function inverse. But loosely speaking, I think what you are looking for is
$$\frac{d^3V}{dx\,dy\,dz}$$
where ##V## is the volume.
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Thanks. That makes sense but I've never seen that kind of notation before. In fact I don't think I've ever seen any notation to cover this. I just thought I was missing something obvious.
I'm reviewing Meirovitch's "Methods of Analytical Dynamics," and I don't understand the commutation of the derivative from r to dr:
$$
\mathbf{F} \cdot d\mathbf{r} = m \ddot{\mathbf{r}} \cdot d\mathbf{r} = m\mathbf{\dot{r}} \cdot d\mathbf{\dot{r}}
$$