For function $\rho(x(t),t)$ total derivative is $$\frac{d\rho}{dt}=\frac{\partial \rho}{\partial t}+\frac{d x}{d t}\frac{\partial \rho}{\partial x}$$
I'm wondering the exact meaning of following statement:
The total derivative notation should be sufficient to indicate when x and $\rho$ are being treated as functions of t on a certain curve. $\frac{d\rho}{d t}=0$ means $\rho$ remains constant on a curve. why?