I have been working on some physics problems, and have realised that I sometimes write a single infinitesimal (or delta) quantity that actually is a product of two independent delta quantities, e.g. $dA=r dr d\phi$ for an area, but equally we have an infinitesimal area even if only one of $r$ or $\phi$ is infinitesimal; as in you might have an arc subtending a non-infinitesimal angle $\phi$ with area $dA=r dr \phi$.
I realise that in physical situations it is generally clear whether the quantity is infinitesimal in one or two quantities, but I was wondering whether mathematicians distinguish between these quantities? It seems to me non-trivial to have an infinitesimal quantity that 'hides' several infintesimals. And could it be possible to break the problem up to have more infinitesimal? I.e. are infuntesimals fundamental in that any infinitesimal quantity is the product of a given number of infinitesimal and not more or less?