This version seems to work also as a palette:

I apologize for "yelling," but I was focussing on/highlighting the issue that seemed to be the source of the misunderstanding. Forgive me.

Your current solution is excellent and acceptable. (I had tried something along those lines with the Basic Math Palette but somehow failed.) I was hoping for a slightly more "mathematical form," such as your typographic form you provided earlier. After all, I've never seen a mathematician write a derivative with the curly brackets and such.

I'll assume your final solution is the best that can be provided and be done with it.

Thanks again.

No no no. The issue isn't just about running code to get the template... it is to get a template THAT CAN THEN BE INTERPRETED BY MATHEMATICA TO CALCULATE THE ACTUAL MULTI-VARIABLE DERIVATIVE.

As background: for example when you enter D[Sin[a x] Cos[ b y], {x, 2}, {y, 3}] you get

-a^2 b^3 Sin[a x] Sin[b y]

In short the actual two-variable symbolic derivative IS COMPUTED.

Great. But here the input is in the unwanted "computer science" form (D[Sin[a x] Cos[ b y], {x, 2}, {y, 3}]) rather than the desired "mathematical typography" form such as provided by the template you created.

But getting the mathematical typography is just HALF my problem: I then want that input form TO BE INTERPRETED (calculated) by Mathematica. Your approach does not achieve that!!! If I fill in your template AND THEN TRY TO CALCULATE THE ACTUAL DERIVATIVE OF SOME FUNCTION, MATHEMATICA FAILS.

Try computing the derivative from your filled-in template to see why your approach does not provide a solution as follows: Execute your code to get the nice mathematical typography as you've shown. Now fill in for the function an example, such as Sin[a x] + Cos[b x]. I'm sure it all looks precisely how I'd like... in a mathematical form that is easy to read by mathematicians. Great.

But now the problem: TRY TO EXECUTE YOUR CODE TO HAVE MATHEMATICA CALCULATE THE ACTUAL DERIVATIVE, to get the result in the above example (-a^2 b^3 Sin[a x] Sin[b y]). Your code does NOT achieve that.

In short, I WANT the solution -a^2 b^3 Sin[a x] Sin[b y] to appear BUT IT DOES NOT. THAT is the problem. (Actually, it is the second HALF of the problem.)

In short (again): Render a multi-variable derivative in the nice mathematical form you have BUT ALSO HAVE THE INPUT INTERPRETABLE BY MATHEMATICA SO THAT THE ACTUAL DERIVATIVE IS CALCULATED.

I don't think I can be any clearer than that.

If you evaluate the code, you will be presented with a template. Fill in the little squares and evaluate. On my system it computes fine.

Maybe something like this?

DisplayForm@FormBox[
    FractionBox[
      RowBox[{
         SuperscriptBox["\[PartialD]", "\[Placeholder]"], 
     "\[Placeholder]"}], 
      RowBox[{
         RowBox[{"\[PartialD]", 
            SuperscriptBox["\[Placeholder]", "\[Placeholder]"]}], 
     "\[ThinSpace]", 
         RowBox[{"\[PartialD]", 
            SuperscriptBox["\[Placeholder]", "\[Placeholder]"]}]}],
      MultilineFunction -> None], TraditionalForm]

It is inspired by the CellExpression of Ahmed's answer. It may be turned into a palette.

Hi David,
Does the video below answer your question?