\DeclareDocumentCommand\partialderivative{ s o m g g d() }
{ % Partial derivative
    % s: star for \flatfrac flat derivative
    % o: optional n for nth derivative
    % m: mandatory (x in df/dx)
    % g: optional (f in df/dx)
    % g: optional (y in d^2f/dxdy)
    % d: long-form d/dx(...)
    \IfBooleanTF{#1}
    {\let\fractype\flatfrac}
    {\let\fractype\frac}
  \IfNoValueTF{#4}
    {
      \IfNoValueTF{#6}
      {\fractype{\partial \IfNoValueTF{#2}{}{^{#2}}}{\partial #3\IfNoValueTF{#2}{}{^{#2}}}}
      {\fractype{\partial \IfNoValueTF{#2}{}{^{#2}}}{\partial #3\IfNoValueTF{#2}{}{^{#2}}} \argopen(#6\argclose)}
    }
    {
      \IfNoValueTF{#5}
      {
        \fractype{\partial \IfNoValueTF{#2}{}{^{#2}} #3}{\partial #4\IfNoValueTF{#2}{}{^{#2}}}
        \IfValueT{#6}{\argopen(#6\argclose)}
      }
      {
        \fractype{\partial^2 #3}{\partial #4 \partial #5}
        \IfValueT{#6}{\argopen(#6\argclose)}
      }
    }
}
\DeclareDocumentCommand\pderivative{}{\partialderivative} % Shorthand for \partialderivative
\DeclareDocumentCommand\pdv{}{\partialderivative} % Shorthand for \partialderivative