Will we obtain an infinitesimal when we neglect $x^2$ in $x+x^2$, as ${x \to 0}$?

Question

Let's assume that we have $2xdx + dx^2$. We can neglect $dx^2$ and we'll obtain $2xdx$.
Let's assume that we have $x+x^2$ and ${x \to 0}$. We can also neglect $x^2$, but will we obtain an infinitesimal $x$ as such as $dx$?

Thanks.