I would be more explicit that dy is a small “slice” or change in y (and similarly for dx), and that because dx is small the difference between y(x) and y(x+dx) can be neglected (with the same being true of their derivatives).

Modern mathematicians don’t like the imprecision of “dx is a small change in x” and so reformulates things, but the differences are completely irrelevant to anything you’re doing in biology. It was good enough for Leibniz.