What does dy/dx represent?

dy/dx represents the gradient of a curve. The d represents an infinitesimally small range so it is essentially as though you are doing change in y over change in x like you would for a y = mx +c graph but over a very small range. This is why if you work out dy/dx for a straight line you would get a number whereas for a curve you will get a function of x as the gradient of the line changes depending where on the curve you are.