I have heard or read that the reason why in calculus dx is seen so often typed as $\mathrm d x$ is because $\mathrm d$ is an operator or a symbol, while $x$ is in cursive because it is a variable. This seems to be the understanding also in this post.
But I'd like to ask for a bit more background about what type of operator $\mathbb d$ is (is it a function, for example?)- I know that in Riemman integrals it serves the purpose of partitioning the $x$ domain into infinitesimally thin slices, but there has to be more to it...
As for the symbol explanation, aren't we always dealing with symbols? Isn't $x$ just as much of a symbol as $\mathrm d$?
Incidentally, I see that there is a question that reads identical to this one, but it refers to a specific situation.
Thanks for the comments - still not clear on how to splice them all... So let me rephrase the question: Is it like this
$$\left. \begin{array}{l} \text{if $d$ is the exterior derivative operator:}&\mathrm dx\\ \text{if $d$ is part of the symbol of an element of }V^*\text{:}&dx \end{array} \right\} $$
?
Here's some informative interaction on the sister community tex.se:
