What Does the d Represent in Differential Quantities?

[Pilpellon]

[Mentor's note: This question was split off from: https://www.physicsforums.com/threads/meaning-of-physical-quantities-and-division.880214/]

What does this differential "d" mean? Why say dE instead of E?

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[Nugatory]

If you look carefully you'll see that there's a $d\omega_i$ in there as well. This formula is telling you how much $E$ will change ($dE$) if you change $\omega_i$ by a little bit ($d\omega_i$). The actual values of $E$ and $\omega_i$ could be pretty much anything as far as this formula is concerned, but whatever they are, if one them is changed by a small amount the other will change by the small amount calculated from the formula.