Infinitesimals can't be used to prove anything - it's really easy to write equations like

x + y + z = 0

dx/dy * dy/dz * dz/dx = -1

that make no sense if you don't know epsilon-delta calculus.

You can use infinitesimal analysis but that's a completely different thing that you probably won't enjoy if you don't think epsilon-delta is straightforward.

https://en.m.wikipedia.org/wiki/Smooth_infinitesimal_analysi...