I have only taken basic real analysis, so to me $\dfrac {dy}{dx}$ is just a formal symbol which stands for the limit of the difference quotient. Now, I know that $dy = y'(x) dx$ has some intuitive meaning historically, but if nowdays it's just another representation for the equation $\dfrac {dy}{dx} = y'(x)$ (which does have a formal meaning), why does it even exist in modern mathematics?
2026-04-25 16:15:12.1777133712
What exactly is the meaning of/why exactly do we write $dy = y'(x) dx$?
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