

this true, but in physics (and in maths too, especially in real analysis), we use differentiation as a equivalent transformation, in a generalised sense. we often come up with ways to define it with something like - finitely many discontinous points or something, which we can iron it. but major problem here (i think) is order of operation - we can not interchange sum and diff when they both depend on x
congrats. I dont read much, but i might consider this one