renewcommand{frac}{mfrac} but in subscript/superscript

Question

Can I renewcommand conditionally if displaystyle, superscript/subscript?
I have:
documentclass[11pt]{article}
usepackage{amsmath}
pagestyle{empty}
usepackage{nccmath}

begin{document}

Equation:
{renewcommand{frac}{mfrac}begin{equation}
   x^{frac{1}{2}}
 +frac{1}{2}
end{equation}}relax

end{document}

I need something like:
begin{equation}
   x^{frac{1}{2}}
 +mfrac{1}{2}
end{equation}

egreg · Accepted Answer

I'm not a fan of mfrac. If you want to use it, do, but use mfrac when you really want it. Whether using mfrac or frac depends on several factors usually involving the formula you want to typeset. For instance, mfrac in front of int would possiblye appear out of place.
Here's a way to cope with the problem and also keep care of not doing wrong things with commands defined via DeclareRobustCommand, for which let is quite dangerous.
documentclass[11pt,twocolumn]{article}
usepackage{amsmath}
usepackage{nccmath}

newififsmallfractions
newcommand{smallfractions}{smallfractionstrue}
newcommand{normalfractions}{smallfractionsfalse}
NewCommandCopy{latexfrac}{frac}

DeclareRobustCommand{frac}[2]{%
  ifsmallfractions
    mathchoice{mfrac{#1}{#2}}%
      {latexfrac{#1}{#2}}%
      {latexfrac{#1}{#2}}%
      {latexfrac{#1}{#2}}%
  else
    latexfrac{#1}{#2}%
  fi
}

begin{document}

Equation:
begin{equation}smallfractions
   x^{frac{1}{2}}
 +frac{1}{2}
end{equation}
Normal equation:
begin{equation}
   x^{frac{1}{2}}
 +frac{1}{2}
end{equation}
Better typesetting:
begin{equation}
   x^{1/2} +tfrac{1}{2}
end{equation}

end{document}

You can declare smallfractions anywhere and it will obey the normal grouping rules.

Steven B. Segletes · Answer

This retains the original size of frac in scriptstyle and scriptscriptstyle, while using mfrac in text and display styles.  Original frac can be recovered using lfrac.
EDITED, per David's suggestion, to account for frac's new-found robustness...using LetLtxMacro instead of a simple let.
documentclass[11pt]{article}
usepackage{amsmath,letltxmacro}
pagestyle{empty}
usepackage{nccmath}
LetLtxMacrolfracfrac
renewcommandfrac[2]{mathchoice
  {mfrac{#1}{#2}}
  {mfrac{#1}{#2}}
  {lfrac{#1}{#2}}
  {lfrac{#1}{#2}}
}
begin{document}

Equation:
begin{equation}
   x^{frac{1}{2}}
 +frac{1}{2} +lfrac{1}{2}
end{equation}
end{document}

renewcommand{frac}{mfrac} but in subscript/superscript

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