For example, I'm very confuse on the fact that physics uses calculus such as, $dA$ as a very small infinitesimal area, where integral of that produce the total Area. Therefore, in a sense, $dA$ is often treated like a variable. However, in calculus, there's such thing such as $d/dx( )$ or $D$ operator, and even Half-derivative that seems confusing in physical context. This operator idea seems to contradict with my picture of "infinitesimal variable". Another thing that I am confused is the idea of high order derivative, if I think in "operator" sense, it is like $d/dx(dy/dx)$ for 2nd order derivative. However, I do not get a meaning about it when apply on physical context, Let's say distance derived respect to time to the 2nd order: $d(dr)/dt^2$, it is like $d(dr)/dt^2$... Infinitesimal of the Infinitesimal of distance? or Infinitesimal changes of the Infinitesimal changes of distance?