How to get an upright \partial?

\usepackage[partialup]{kpfonts}

or if you do not want to load the kpfonts:

\documentclass{scrartcl}
\usepackage[T1]{fontenc}
\makeatletter
\newif\ifkp@upRm% is used in the .fd-file of jkp
\DeclareSymbolFont{Letters}{OML}{jkp}{m}{n}
\DeclareMathSymbol{\partialup}{\mathord}{Letters}{128}
\makeatother
\usepackage{mathptmx}

\begin{document}

\[ \frac{\partialup f}{\partialup x} \]

\end{document}

Another nice approach could be rotating and scaling the \partial symbol by this one-liner:

\DeclareRobustCommand{\uppartial}{\text{\rotatebox[origin=t]{20}{\scalebox{0.95}[1]{$\partial$}}}\hspace{-1pt}}

It uses the normal partial symbol, squeezes it a bit horizontally, rotates it around the top for 20 deg and minimizes the distance to the following symbol.

Now you can use \uppartial in your math environment and get nice results like this:

For Germans: DIN 1338 regulates which symbols are written in italics and which ones upright (see de:Wikipedia)

You can get upright partial symbol in Computer Modern the following way

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{bm}
\usepackage{amsmath}
\usepackage{amssymb}
\newsavebox{\foobox}
\newcommand{\slantbox}[2][0]{\mbox{%
    \sbox{\foobox}{#2}%
    \hskip\wd\foobox
    \pdfsave
    \pdfsetmatrix{1 0 #1 1}%
    \llap{\usebox{\foobox}}%
    \pdfrestore
}}
\newcommand\unslant[2][-.25]{\slantbox[#1]{$#2$}}

\newcommand{\uppartial}{\unslant\partial}
\newcommand{\upPartial}{\unslant\partial\kern-0.8pt}


\begin{document}

$$\bm{E} = -\left( \frac{\uppartial  V}{\uppartial x} \bm{\hat{\imath}} +                 \frac{\uppartial V}{\uppartial y}\bm{\hat{\jmath}} + \frac{\uppartial V}    {\uppartial z}\bm{\hat{k}} \right)$$\\

$$\bm{E} = -\left( \frac{\upPartial  V}{\upPartial x} \bm{\hat{\imath}} +     \frac{\upPartial V}{\upPartial y}\bm{\hat{\jmath}} + \frac{\upPartial V}{\upPartial z}\bm{\hat{k}} \right)$$\\

$$\bm{E} = -\left( \frac{\partial  V}{\partial x} \bm{\hat{\imath}} + \frac{\partial V}{\partial y}\bm{\hat{\jmath}} + \frac{\partial V}{\partial z}\bm{\hat{k}} \right)$$

\end{document}

This is taken from this answer.