Can I have a flexible partial derivative macro?

Question

I was thinking about writing a partial derivative macro that has a similar syntax to the Mathematica D function. (example)

The syntax could be like this:

• \D{f}{x} expands to \frac{\partial f}{\partial x}
• \D{f}{x,y} expands to \frac{\partial^2 f}{\partial x\,\partial y}
• \D{f}{{x,2},y} expands to \frac{\partial^3 f}{\partial x^2\,\partial y}
• et cetera for any number of derivatives.

Bonus points for an optional argument so that for instance

• \D[subscript]{f}{{x,2},y} expands to f_{xxy}

I looked at the commath package but the syntax is a little tedious. For instance, to get \frac{\partial^3 f}{\partial x^2\,\partial y} with that package I would need to do \md{f}{3}{x}{2}{y}{}. And it doesn't generalize to three variables.

Before I dive in I thought I'd ask the hive and see what's been done.

Answer 1

The cool package offers commands for writing partial derivates (and a lot of other stuff).

A short example:

\documentclass{article}
\usepackage{cool}
\begin{document}
\begin{equation*}
  \pderiv{f}{x} \qquad
  \pderiv[2,3]{f}{x,y} \qquad
  \pderiv[1,n,4]{f}{x,y,z}
\end{equation*}
\end{document}

Note

By default the last two of those will not work, as there is a bug in the package. This can be fixed by changing a \def to \edef in line 2059 of cool.sty, see Basic use of derivative with cool package fails with "Missing \endcsname inserted"

Answer 2

I have this, which is quite similar to what you want:

\documentclass[a4paper]{article} 

\makeatletter 
\newcommand{\der}[2]{\begingroup 
  \@tempswafalse\toks@={}\count@=\z@ 
  \@for\next:=#2\do 
    {\expandafter\check@var\next
     \advance\count@\der@exp 
     \if@tempswa 
       \toks@=\expandafter{\the\toks@\,}% 
     \else 
       \@tempswatrue 
     \fi 
     \toks@=\expandafter{\the\expandafter\toks@\expandafter\partial\der@var}}% 
  \frac{\partial\ifnum\count@=\@ne\else^{\number\count@}\fi#1}{\the\toks@}% 
  \endgroup} 
\def\check@var{\@ifstar{\mult@var}{\one@var}} 
\def\mult@var#1#2{\def\der@var{#2^{#1}}\def\der@exp{#1}} 
\def\one@var#1{\def\der@var{#1}\chardef\der@exp\@ne} 
\makeatother 

\begin{document} 
\[ 
\der{f}{x}\qquad \der{f}{*{2}{x},y}\qquad \der{f}{*{3}{x},y,*{4}{z}} 
\] 
\end{document}

EDIT: the following code will render correctly also

\pder{f}{\mathbf{x}}
\pder{f_1}{x_1}

Here it is:

\makeatletter 
\newcommand{\der}[2]{\begingroup 
  \@tempswafalse\toks@={}\count@=\z@ 
  \@for\next:=#2\do 
    {\expandafter\check@var\next\@nil
     \advance\count@\der@exp 
     \if@tempswa 
       \toks@=\expandafter{\the\toks@\,}% 
     \else 
       \@tempswatrue 
     \fi 
     \toks@=\expandafter{\the\expandafter\toks@\expandafter\partial\der@var}}% 
  \frac{\partial\ifnum\count@=\@ne\else^{\number\count@}\fi#1}{\the\toks@}% 
  \endgroup} 
\def\check@var{\@ifstar{\mult@var}{\one@var}} 
\def\mult@var#1#2\@nil{\def\der@var{#2^{#1}}\def\der@exp{#1}} 
\def\one@var#1\@nil{\def\der@var{#1}\chardef\der@exp\@ne} 
\makeatother 

Answer 3

The esdiff package should not go unmentioned in this context.

In the meantime there are two other packages which facilitate easy typesetting of derivatives.

• bropd
• physics

Answer 4

Here my try. I prefer a more simply input format: \Der{<var>}{<var><num>,<var><num>,...} e.g. \Der{f}{x3,y,z4}. This also works for more complicated input like \Der{f}{{\hat{x}}3,y105}.

\documentclass{article}

\makeatletter

\newcommand\Der[2]{%
    \begingroup
    \@temptokena{\@gobble}%
    \@tempcnta\z@
    \@for\var:=#2\do{%
        \expandafter\@Der\var\relax
    }%
    \ensuremath{\frac{\partial
    \ifnum\@tempcnta>\@ne
        ^{\the\@tempcnta}%
    \fi
    #1}{\the\@temptokena}}%
    \endgroup
}

\def\@Der#1#2\relax{%
    \ifx\relax#2\relax
        \advance\@tempcnta by \@ne
        \@temptokena\expandafter{\the\@temptokena\,\partial{#1}}%
    \else
        \advance\@tempcnta by #2\relax
        \@temptokena\expandafter{\the\@temptokena\,\partial{#1}^{#2}}%
    \fi
}

\makeatother

\usepackage{amsmath}
\begin{document}

\[
\Der{f}{x}
\qquad
\Der{f}{x,y}
\qquad
\Der{f}{x2,y}
\]

\[ 
\Der{f}{x}\qquad \Der{f}{x2,y}\qquad \Der{f}{x3,y,z4} 
\]

\[ 
\Der{f}{{\hat{x}}3,y1,z10} 
\]

\end{document}

---

It is also possible to avoid the need for commas. I'm thought first this is more readable but I'm not sure about that anymore. This version doesn't support negative numbers (no loss) and might be a little more sensitive than the first.

\documentclass{article}

\makeatletter

\newcommand\Der[2]{%
    \begingroup
    \@temptokena{\@gobble}%
    \@tempcnta\z@
    \expandafter\@Der@var#2\relax
    \ensuremath{\frac{\partial
    \ifnum\@tempcnta>\@ne
        ^{\the\@tempcnta}%
    \fi
    #1}{\the\@temptokena}}%
    \endgroup
}

\def\@Der@var#1{%
    \ifx\relax#1\empty\else
        \def\next{\expandafter\@Der@num\expandafter{\the\@tempcntb}{#1}}%
        \afterassignment\next
        \@tempcntb=0%
    \fi
}

\def\@Der@num#1#2{%
    \ifnum#1=\z@
        \advance\@tempcnta by \@ne
        \@temptokena\expandafter{\the\@temptokena\,\partial{#2}}%
    \else
        \advance\@tempcnta by #1\relax
        \@temptokena\expandafter{\the\@temptokena\,\partial{#2}^{#1}}%
    \fi
    \@Der@var
}

\makeatother

\usepackage{amsmath}
\begin{document}

\[
\Der{f}{x}
\qquad
\Der{f}{xy}
\qquad
\Der{f}{x2y}
\]

\[ 
\Der{f}{x}\qquad \Der{f}{x2y}\qquad \Der{f}{x3 y z4} 
\]

\[ 
\Der{f}{{\hat{x}}3y1z10} 
\]

\end{document}

---

Result (for both implementations):

Answer 5

Since 2019-07-21 there is another package that allows to write, in a rather simple fashion, derivatives or partial derivatives. This package is namely derivative. Here are some examples, taken from the manual:

\documentclass[12pt]{article}
\usepackage{derivative,mathtools}
\begin{document}
\[
\begin{aligned}
\odv{y}{x}\\ 
\odv*{y}{x}\quad \texttt{switch-*=false}\\ 
\odv[n]{y}{x}\\ 
\odv{y}/{x}\\ 
\odv{y}{x}_{a}\\
\odv{y}{x}^{b}\\
\odv{y}{x}^{b}_{a}\\
\pdv{f}{x,y}\\
\pdv*{f}{x,y}\\
\pdv{ f(x,y,z) }{ x, y, z }\\
\end{aligned}
\]
\end{document}