I recall trying to do this, but in the end I gave up. I suppose you know the inherent ambiguity of expressions like
${\partial f \over \partial q} (t, t)$, and I suppose you avoid that in your work. Here's a way to do what you show:
Format[Derivative[1, 0][f_][a_, b_]] := HoldForm[D[f[a, b], x]];
TeXForm will use this FormatValue:
D[g[x, y], x]
% /. x -> 7 // TeXForm
(*
\!\(
\*SubscriptBox[\(\[PartialD]\), \(x\)]\(g[x, y]\)\)
\frac{\partial g(7,y)}{\partial x}
*)
First-order, higher-order and zero-order each usually get typeset differently. It's not clear whether you need only first-order derivative, or a way to handle all derivatives. As I said, I gave up on handling all derivatives.
