Correct typography for using Leibniz Notation

Question

What is the correct way of writing derivatives in notation form? Should the 'd' be upright or italic, that is $\mathrm d$ or $d\,$? As an example, should we write: $$ \frac {\mathrm dy}{\mathrm dx}\qquad\text{or}\qquad \frac {dy}{dx} \, \text ?$$

I feel the first method (upright 'd') is correct, since italic letters are generally used for variables, but most people (and Wikipedia) use the italic 'd'. Which is actually more correct?

Also, how do we use this notation on notebooks (writing by hand), while avoiding potential confusion in a variable $d$ and the differential symbol? Since mostly we write variables upright on notebooks, so $\displaystyle \mathrm{\frac{dd}{dt}}$ in a notebook would be potentially confusing. (Of course, we could avoid a variable 'd', but still, what would be another way out of this?)

Answer 1

It is most common to use italic $d$, probably at least in part because that's the default LaTeX does. I have adopted a habit of handwriting with cursive to help distinguish symbols.

I write mostly in print, but I write $dx$ cursive and conjoined, which emphasizes that the two letters form one mathematical symbol. I write the differential operator as a cursive $d$ not conjoined with the following text.