Any introductory calculus book worth the paper it’s printed on would gladly tell you that the differential of the function y = x at a point x0 is nothing more than x - x0 and that you do not have to think about it as something that is “infinitely small” or anything equally mysterious. (Some would even go as far as saying that “the differential of a function of one variable is a linear map of the increment of the argument.”) So, with dx = x - x0, you can do with it anything you want, even divide by it (assuming that dx stays non-zero).