And that's essentially what this definition of the limit is telling us, especially as delta x approaches zero, we're going to have a super small change in x as delta x approaches zero, and then we're gonna have a resulting super small change in y. So that's one way that you can feel a little bit better of, and this is actually one of the justifications for this type of notation, is you could view this, what's the resulting super small, or what's the super small change in y for a given super small change in x, which is giving us the sense of what's the limiting value of the slope as we go from the slope of a secant line to a tangent line. And if you view it that way, you might feel a little bit better about using the differentials or treating them algebraically, whereas, okay, let me just multiply both sides by that super small change in x. So the big picture is this is a technique that you will often see in introductory differential equations classes, introductory multivariable classes, and introductory calculus classes, but it's not very mathematically rigorous to just treat differentials like algebraic expressions, but even though it's not very mathematically rigorous to do it willy-nilly like that, it has proven to be very useful. Now, as you get more sophisticated in your mathematics, there are rigorous definitions of a differential where you can get a better sense of where it is mathematically rigorous to use it and where it isn't. But the whole point here is if you felt a little weird feeling about multiplying both sides by dx or dividing both sides by dx or dy, your feeling is mathematically justified because it's not a very rigorous thing to do, at least until you have more rigor behind it. But I will tell you that if you're an introductory student, it is a reasonable thing to do as you explore and manipulate some of these basic differential equations.