Surely you understand the concept of a rate being "The change in the Dependent Variable per unit change in the Independent Variable". Which is the DV and which is the IV?
someone could correct me but I see it as
For a function f(x), if f is in widgets and x is in blivets, what are the units of the derivative f ' (x), widgets per blivet or blivets per widget?
derivative of widgets (y) with respect to blivets(x) so it's ...what do you think?