Concept: $d \vec r$ is a small displacement vector (editing)

One typical notation used for derivatives is Leibniz notation ($e.g.,$ $df/dx$).  Physicists often think of the $df$ and $dx$ as distinct quantities (``differentials'') that can be measured, calculated, and manipulated independent of one another.  In particular, a differential can be thought of as the (small) change in a quantity when a small change is made to a physical system.  A differential can also be thought of as the difference between the values of a quantity between two different (nearby) physical states. This line of thinking is also valuable for thinking about integration in physical situations.