Add missing () to mathematical functions

Question

I am trying to get LaTeX to render

${f}^\prime = e^{x\,\log \cos x}\,\left(x\,\log \cos x\right)^\prime$

as

${f}^\prime = e^{x\,\log \left (\cos \left (x  \right )  \right )}\,\left(x\,\log \left (\cos \left (x  \right )  \right )\right)^\prime$

thus automatically adding the missing (). If the functions have more than one argument, the parentheses will already be added (so there's no ambiguity). Does anyone know a quick and simple way to accomplish this?

Answer 1

The following works if you always write \log \cos x

\documentclass{article}
\let\Log\log
\def\log \cos x{\Log(\cos(x))}     
\begin{document}

${f}^\prime = e^{x\,\log \cos x}\,(x\,\log \cos x)^\prime$

\end{document}

Answer 2

Not completely, what you wanted, but almost:

\documentclass{article}

\newcommand*{\redefinesymbolwitharg}[1]{%
  \expandafter\newcommand\csname ltx#1\endcsname{}%
  \expandafter\let\csname ltx#1\expandafter\endcsname\csname #1\endcsname
  \expandafter\renewcommand\csname #1\endcsname[1]{%
   \csname ltx#1\endcsname\left(##1\right)%
 }%
}

\redefinesymbolwitharg{cos}
\redefinesymbolwitharg{log}

\begin{document}

% You may use \ltxcos, \ltxlog etc. if you need the original definition
% without argument:
${f}^\prime = e^{x \ltxlog \left (\ltxcos \left (x  \right )  \right  )}\,\left(x \ltxlog \left (\ltxcos \left (x  \right )  \right )\right)^\prime$

% But \cos and \log expect an argument now:
${f}^\prime = e^{x \log{\cos x}}\,\left(x \log{\cos x}\right)^\prime$

\end{document}

Here for the argument of \cos I've used the standard behavior of TeX, that if you don't use argument braces {…} it uses the first token after the command to be the argument. This would work with each single characters coded with a single byte (e.g. \cos ß would fail if you're using \usepackage[utf8]{inputenc} but \cos{ß} or \cos \beta would be correct).

And if you prefer to write \redefinesymbolwitharg\cos instead of \redefinesymbolswitharg{cos} you may replace definition of \redefinesymbolwitharg by:

\makeatletter
\newcommand*{\redefinesymbolwitharg}[1]{%
  \edef\@tempa{\expandafter\@gobble\string #1}%
  \expandafter\let\csname ltx\@tempa\expandafter\endcsname\csname \@tempa\endcsname
  \expandafter\renewcommand\csname \@tempa\endcsname[1]{%
    \csname ltx\@tempa\endcsname\left(##1\right)%
  }%
}
\makeatother

Answer 3

Mark's suggestion is a good one. But if you don't want to deal with \newcommand you can add the "()" without \left of \right as follows:

 $ f^\prime = e^{x\,\log (\cos (x))}\,(x\,\log (\cos (x)))^\prime $

The result is almost exactly what you want except for a little difference in the space preceding the brackets.

Answer 4

I think Mark's suggestion is the way to go. But, you do need to be aware that there are problems unless you enclose the args of the \cos within a {} when there is more than one character involved as in the last case here.

This is no different than other functions if you leave out the {} as in $\frac 12a$,

\documentclass{article}

\newcommand{\Cos}[1]{\cos\left(#1\right)}%
\begin{document}
${f}^\prime = e^{x\,\log \cos x}\,\left(x\,\log \cos x\right)^\prime$

${f}^\prime = e^{x\,\log \left (\cos \left (x  \right )  \right )}\,\left(x\,\log \left (\cos \left (x  \right )  \right )\right)^\prime$

\bigskip
Now using \textbackslash{}Cos:\par
${f}^\prime = e^{x\,\log \Cos x}\,\left(x\,\log \Cos x\right)^\prime$

${f}^\prime = e^{x\,\log \Cos {x\pi}}\,\left(x\,\log \Cos {x\pi}\right)^\prime$
\end{document}