This is not true. The usual calculus that people learn (and usually learn with rigor in a real analysis course) does not touch infinitesimals. The approach via

This is not true. The usual calculus that people learn (and usually learn with rigor in a real analysis course) does not touch infinitesimals. The approach via infinitesimals is even called "nonstandard analysis". https://en.wikipedia.org/wiki/Nonstandard_analysis https://en.wikipedia.org/wiki/Nonstandard_analysis