When I take derivatives in math I think of it as the amount of infinitesimals that change in one variable with respect to another, when the latter changes by one infinitesimal. But in physics those variables have real life meanings, so when I take the derivative of position with respect to time I feel like I am asking myself how many infinitesimals of time change in distance. Which is kind of weird. Is that because all infinitesimals are the same? Like: dx=dt=dy=dz? And even if that's not the explanation for this particular question; are they all the same? Are the infinitesimals of all variables basically 1/∞? Anyway; or is it that some mathematical equation just happens to explain a physical occurrence? Like, we just assign real meanings to abstract variables and the derivatives are actually speaking of the variables, and only as a consequence about the physical meaning we assign to them?