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?)
esdiff
package does it by default (including for partial derivatives) and has a simple syntax, useful for higher order derivatives. Often people use italic letters by pure laziness. $\endgroup$