LaTeX Macro

Preamble

To use the specular differentiation symbol in your LaTeX document, add the following code to your preamble (before \begin{document}):

% Required packages
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{amssymb}

% specular derivative symbol
\newcommand{\sd}{\mathord{\prime\mkern-2.5mu\reflectbox{$\scriptstyle\prime$}}}

% specular Gateaux derivative symbol
\newcommand{\sGd}{%
    \mathord{\text{\normalfont\UseTextSymbol{T1}{\dj}}}%
}

% specular Frechet derivative symbol
\newcommand{\sFd}{%
    \mathord{\text{\normalfont\UseTextSymbol{T1}{\DJ}}}%
}

% specular gradient symbol
\newcommand{\sg}{%
  \mathchoice
    {\mathord{\raisebox{-0.05ex}{\rule{0pt}{1.3ex}\smash{\scalebox{1.37}[1.22]{\ensuremath{\displaystyle\blacktriangledown}}}}\mkern-1.2mu}}
    {\mathord{\raisebox{-0.05ex}{\rule{0pt}{1.3ex}\smash{\scalebox{1.37}[1.22]{\ensuremath{\textstyle\blacktriangledown}}}}\mkern-1.2mu}}
    {\mathord{\raisebox{-0.03ex}{\rule{0pt}{1.0ex}\smash{\scalebox{1.29}[1.15]{\ensuremath{\scriptstyle\blacktriangledown}}}}\mkern-0.8mu}}
    {\mathord{\raisebox{-0.02ex}{\rule{0pt}{0.8ex}\smash{\scalebox{1.18}[1.05]{\ensuremath{\scriptscriptstyle\blacktriangledown}}}}\mkern-0.5mu}}
}

The packages above support the following commands:

Package	Purpose
`fontenc` with `T1`	Provides the `đ` and `Đ` text symbols used by `\sGd` and `\sFd`.
`amsmath`	Provides `\text` for `\sGd` and `\sFd`.
`graphicx`	Reflects the prime in `\sd` and scales the triangle in `\sg`.
`amssymb`	Provides `\blacktriangledown` for `\sg`.

If you only use \sGd and \sFd, you only need fontenc with T1 and amsmath from this list. Do not load a package again if your document already loads it.

Usage examples

Use the symbols in your document after \begin{document}.

% A specular derivative in the one-dimensional Euclidean space
$f^{\sd}(x)$

% A specular directional derivative in normed vector spaces
$\partial^{\sd}_v f(x)$

% A specular Gateaux derivative
$\sGd f(x)$

% A specular Frechet derivative
$\sFd f(x)$

% A specular gradient
$\sg f(x)$

Markdown usage

The documentation defines \sd, \sGd, \sFd, and \sg globally, so the same commands work inside Markdown math without adding a preamble to each page. The Gâteaux and Fréchet symbols are the upright letters đ and Đ, respectively.

Markdown source	Rendered symbol
`\(f^{\sd}(x)\)`	\(f^{\sd}(x)\)
`\(\partial^{\sd}_v f(x)\)`	\(\partial^{\sd}_v f(x)\)
`\(\sGd f(x)\)`	\(\sGd f(x)\)
`\(\sFd f(x)\)`	\(\sFd f(x)\)
`\(\sg f(x)\)`	\(\sg f(x)\)
`\(\frac{\sg f(x)}{\\|\sg f(x)\\|}\)`	\(\frac{\sg f(x)}{\\|\sg f(x)\\|}\)