$\sin$ vs. $sin$ - history and usage

$\LaTeX$ was set down while the conventions were different, and to preserve the older texts, the rules have not been changed. However, it could be possible for someone to write some .sty file that implements the sort of definitions at the particular date, eg math2000.sty or something, with \renewcommand{vec}[1]{\mathbf{#1}} and \newcommand{dif}[1]{\mathrm{d}#1} and \newcommand{ddif}[2]{\frac{\mathrm{d}#1}{\mathrm{d}#2}.

Then you put something like ddif{q}{t} to get the desired result.

Because the thing has a date in it, and invoked by \usepackage{} then it is more robust to formatting changes &c.

But \operatorname{} is a bit long, and i reassign this to \fn{}, eg \fn{isi}(values).