Also, the author includes an example of \int xyzdx and makes a note of using appropriate spacing. It is my impression that commonly the differential operator is typeset differently, that is: \mathrm{d}x.
Otherwise, great tips.
There is a better way to do this, which is to use LaTeX's built in spacing adjustment, which is different around different types of object (e.g. notice how ab+cd already looks right). To do that, use: \mathop{\mathrm{d}#1}
Even if you carefully do the "right thing", the spacing in LaTeX is by no means perfect. E.g. just look at f(x)g\left(\frac{x}{y}\right) - it looks like g is more associated with f's arguments than its own.
Also, you are right about using \mathrm{d}x. Another friend also just flagged it to me as well, I will update the post regarding this!
> ISO 80000-2:2009 > Quantities and units — Part 2: Mathematical signs and symbols to be used in the natural sciences and technology
https://nhigham.com/2016/01/28/typesetting-mathematics-accor...
TIL
In many articles, there isn't even spacing around differentials. That doesn't mean that is correct too. It just means that, like upright d, the author has more pressing issues than small details of typesetting.
It similar to how vectors (in physics / applied maths) are represented by upright bold letter. Historically, these were bold-italic - the same as how most variables are italic. But early versions of TeX only supported fonts in regular, italic and bold - no bold italic variants existed (even now, bold italics are not universally available for Greek characters). So people used upright bold for vectors, and now it's assumed that it was deliberate.