3

I need a symbol in Latex that I can represent the inexact partial. I need the partial with a bar in the partial.

5

The bar is character octal 26; some playing with kerns does the job: the width of the bar is 9mu, so at the end there's no advance when the \partial symbol is typeset.

\documentclass{article}

\newcommand{\ipartial}{{\mkern4.5mu\mathchar'26\mkern-13.5mu\partial}}

\begin{document}

$x\ipartial f$

$x\partial f$

\end{document}

enter image description here

A less efficient definition if you need to use the symbol also at smaller sizes (\scriptstyle or \scriptscriptstyle):

\documentclass{article}

\newcommand{\ipartial}{%
  {\mathchoice
   {\mkern4.5mu\mathchar'26\mkern-13.5mu\partial}
   {\mkern4.5mu\mathchar'26\mkern-13.5mu\partial}
   {\mkern4mu\mathchar'26\mkern-13mu\partial}
   {\mkern3.25mu\mathchar'26\mkern-12.25mu\partial}
  }%
}

\begin{document}

$x\ipartial f$

$x\partial f$

$\scriptstyle\ipartial\scriptscriptstyle\ipartial$

\end{document}

enter image description here

If you don't plan to use the symbol in \scriptscriptstyle, you can use

\newcommand{\ipartial}{{%
  \mkern4mu\nonscript\mkern0.5mu
  \mathchar'26
  \mkern-13mu\nonscript\mkern-0.5mu
  \partial
}}

that's as efficient as the simple version at the top, and provides the same kerning as the second (less efficient) version in \displaystyle, \textstyle and \scriptstyle.

2

This should yield the same spacing as \partial and supports the smaller math sizes.

\documentclass{article}
\usepackage{stackengine,scalerel}
\def\mpartial{\ThisStyle{\stackinset{r}{-.4\LMex}{c}{-.2\LMex}{%
  $\SavedStyle\mathchar'26$}{$\SavedStyle\partial$}}}
\begin{document}
\[
x \partial f
\]
\[
x \mpartial f
\]
\[
\scriptstyle x \mpartial f
\]
\[
\scriptscriptstyle x \mpartial f
\]
\end{document}

enter image description here

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