(dy/dx) has a very similar meaning to delta(y)/delta(x), that is, the ratio of change in Y to a correspondent change in a variable X. The neat thing though, is that for (dy/dx) this analysis is made for variations of X, that is, for delta(x)'s, that are arbitrarily close to 0 (but are NOT 0) and can, therefore, offer us a rate of change in Y in face of a change in X at ANY given point of analysis, instead of an average over a time period as is the case for delta(y)/delta(x).