Basic code: it evaluates to a template button:
In[]:=
PasteButton@DisplayForm@FormBox[RawBoxes@FractionBox[RowBox[{SuperscriptBox["∂",""],""}],RowBox[{RowBox[{"∂",SuperscriptBox["",""]}],"",RowBox[{"∂",SuperscriptBox["",""]}]}],MultilineFunction->None],TraditionalForm]
Out[]=

∂

∂


∂


Clicking on the template button this get pasted into the insertion point:

∂

∂


∂


Then fill in the square placeholders, one at a time:
3
∂

∂


∂


3
∂
(
2
x
3
y
)
∂


∂


3
∂
(
2
x
3
y
)
∂

x
∂


3
∂
(
2
x
3
y
)
∂
1
x
∂


3
∂
(
2
x
3
y
)
∂
1
x
∂

y
3
∂
(
2
x
3
y
)
∂
1
x
∂
2
y
Evaluate:
In[]:=
3
∂
(
2
x
3
y
)
∂
1
x
∂
2
y
Out[]=
12xy
You can generate a palette:
In[]:=
CreatePalette@PasteButton@DisplayForm@FormBox[RawBoxes@FractionBox[RowBox[{SuperscriptBox["∂",""],""}],RowBox[{RowBox[{"∂",SuperscriptBox["",""]}],"",RowBox[{"∂",SuperscriptBox["",""]}]}],MultilineFunction->None],TraditionalForm]
Out[]=
NotebookObject
Untitled-16
