What derivatives tell us is actually the change in proportion of one thing compared to another. Let's say a function of height y = x squared. now the derivative y' = 2x. Now if I say "x" refers to width that'd mean height "y" would increase two times as much as the width we have. Now imagine 2 points very close to each other so that you can't see by the naked eye and the distance between these two points is shown by a tangent, you can then find quantitatively and qualitatively the change of your height y between these two points when you move infinitesimally across the width x. Now change the height and width with mass, stock price etc.
