Slanted letter in mathmode keeping current style

Question

I'm trying to make a slanted roman d to use in math mode. Using How can I use the slanted variant of the libertine font? I've managed to get it to mostly work, but I don't know how to account for changes in math styles (normal/subscript etc.).

You can see the issue in the extra space after the \dd in the subscript

I've tried using \count0=\fam then \sbox{\diffdbox}{$\fam=\count0 \mathrm{d}$} however that didn't change anytning. Would anybody have any ideas?

\documentclass{article}

\usepackage{mathtools}

\newsavebox\diffdbox
\newcommand{\dd}{%
\sbox{\diffdbox}{$\mathrm{d}$}%
\hskip\wd\diffdbox
\pdfsave%
\pdfsetmatrix{1 0 0.2 1}%
\mathllap{\mathrm{d}}%
\pdfrestore}

\begin{document}

\[
    d \mathrm{d} d
\]
\[
    d \dd d
\]
\[
    x_{d \mathrm{d} d}
\]
\[
    x_{d \dd d}
\]

\end{document}

Answer 1

I'm afraid to ask what would be the usage of the symbol.

There's a much easier way: define a slanted math alphabet.

\documentclass{article}

\usepackage{mathtools}

\DeclareMathAlphabet{\mathsl}{\encodingdefault}{\familydefault}{m}{sl}
\SetMathAlphabet{\mathsl}{bold}{\encodingdefault}{\familydefault}{bx}{sl}

\newcommand{\dd}{\mathsl{d}}

\begin{document}

\begin{gather*}
    d \mathrm{d} d
\\
    d \dd d
\\
    x_{d \mathrm{d} d}
\\
    x_{d \dd d}
\end{gather*}
\boldmath
\begin{gather*}
    d \mathrm{d} d
\\ 
    d \dd d
\\ 
    x_{d \mathrm{d} d}
\\ 
    x_{d \dd d}
\end{gather*}

\end{document}

If you really want to manually slant the symbol (I can't understand why not using italics), use \mathpalette:

\documentclass{article}

\usepackage{mathtools}

\newsavebox\diffdbox
\newcommand{\dd}{{\mathpalette\makesl{d}}}
\newcommand{\makesl}[2]{%
  \begingroup
  \sbox{\diffdbox}{$\mathsurround=0pt#1\mathrm{#2}$}%
  \pdfsave
  \pdfsetmatrix{1 0 0.2 1}%
  \rlap{\usebox{\diffdbox}}%
  \pdfrestore
  \hskip\wd\diffdbox
  \endgroup
}

\begin{document}

\[
    d \mathrm{d} d
\]
\[
    d \dd d
\]
\[
    x_{d \mathrm{d} d}
\]
\[
    x_{d \dd d}
\]

\end{document}