Sans-serif partial derivative symbol?

How about using cmbright to get sans serif math and rotating the \partial?

\documentclass{article}
\usepackage{cmbright}
\usepackage{graphicx}
\newcommand{\upartial}{\rotatebox[origin=c]{15}{\ensuremath{\partial\mkern-2mu}}}
\begin{document}
\[\frac{\partial x}{\partial t}\quad\textnormal{vs.}\quad\frac{\upartial x}{\upartial t}\]
\end{document}

Edit:

One can get cmbright only in math mode with the following code. However, in doing so I discovered this solution is not very robust. As you can see in the image, the upright \partial gets typeset in \displaystyle despite being inside \(...\).

Code:

\documentclass{amsart}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{lmodern,cmbright}
\renewcommand*\familydefault{\rmdefault}
\usepackage{graphicx}
\newcommand{\upartial}{\mathsurround=0pt \rotatebox[origin=c]{15}{$\partial\mkern-2mu$}}
\begin{document}
Normal vs.\ upright partial: \(\frac{\partial x}{\partial t}\) vs.\ \(\frac{\upartial x}{\upartial t}\)
\end{document}

Note: I've also changed the definition of \upartial after reading @egreg's answer here, but the inline math problem persists.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{kpfonts}
\def\uppartial{{\mathversion{sf}\ensuremath{\partialup}}}
\begin{document}
$\partial$ partial derivative symbol in \LaTeX

\sffamily
\uppartial{} partial derivative symbol in \LaTeX
\end{document}

You can also use \usepackage[partialup]{kpfonts} if you do not need the default version. Then \partial is upright by default.

In 2024, if you're willing to use LuaLaTeX, XeLaTeX, ConTeXt, OpTeX, or any engine which supports OpenType Math, you can use the New Computer Modern Sans Math font.

\documentclass{article}

\PassOptionsToPackage{math-style=ISO, bold-style=ISO, sans-style=italic, nabla=upright, partial=upright, warnings-off={mathtools-colon,mathtools-overbracket}}{unicode-math}
\usepackage[sansdefault]{fontsetup}
\usepackage[sans]{dsfont}
\let\symbb\mathds
\let\mathbb\mathds
\renewcommand{\i}{\symup{i}}
\renewcommand*{\hbar}{\mathrm{^^^^0127}}

\begin{document}
    The position space Schrödinger equation for a single non-relativistic particle in one dimension is
    \[
        -\i \hbar \frac{\partial}{\partial t} \Psi (x, t) = \bigg[-\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + V(x, t)\bigg]\Psi(x, t).
    \]
\end{document}

With Open Type math font Lete Sans Math:

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{LeteSansMath.otf}[partial=upright]
\begin{document}

\[\frac{\partial f}{\partial x} = \frac{\partial f}{\partial y}\]

\end{document}

If you only want \partial to be in sans-serif style, you can use the range option provided by unicode-math:

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{latinmodern-math.otf}
\setmathfont{LeteSansMath.otf}[range={\partial}]
\begin{document}
$\frac{\partial f}{\partial x} = \frac{\partial f}{\partial y}$
\end{document}

A solution with sansmathfonts:

\documentclass[12pt]{article}
\usepackage{amsmath,amssymb}
\usepackage{sansmathfonts}
\begin{document}
\begin{align}
    % Linear wave equation
    \frac{\partial u}{\partial t} + c \frac{\partial u}{\partial x} &= 0, \quad \text{(linear wave equation)} \\
    % Wave equation
    \frac{\partial^2 u}{\partial t^2} - c^2 \frac{\partial^2 u}{\partial x^2} &= 0, \quad \text{(wave equation)} \\
    % Gauss's law in differential form
    \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0}, \quad \text{(Gauss's law in differential form)} \\
    % Laplace's equation
    \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} &= 0, \quad \text{(Laplace's equation)}.
\end{align}
\end{document}