How to write partial differential equation (Ex. dQ/dt=ds/dt) with real partial derivative signs?

Question

I would like to make a partial differential equation by using the following notation:

dQ/dt

(without / but with a real numerator and denomenator). Earlier today I got help from this page on how to u_t, but now I also have to write it like dQ/dt. I understand how it can be done by using dollarsigns and fractions, but is it possible to do it using

\begin{equation}
....
\end{equation}

so that it can be on separate lines and using math-style?

See also cool: "The package (COntent Oriented LaTeX) gives LaTeX the power to retain mathematical meaning of its expressions in addition to the typsetting instructions; essentially separating style from the content of the math." — Mike Renfro, Jan 29 '15 at 14:20

score 211 · Accepted Answer · 2015-01-29T13:29:13.153

211

You said partial differential equation:

\documentclass{article}
\begin{document}
\begin{equation}
\frac{\partial Q}{\partial t} = \frac{\partial s}{\partial t}
\end{equation}
\end{document}

enter image description here

now using physics package, extra goodies (bonus):

\documentclass{article}
\usepackage{physics}
\begin{document}
\[
\dv{Q}{t} = \dv{s}{t}  \quad
\dv[n]{Q}{t} = \dv[n]{s}{t}  \quad
\pdv{Q}{t} = \pdv{s}{t}  \quad
\pdv[n]{Q}{t} = \pdv[n]{s}{t}  \quad
\pdv{Q}{x}{t} = \pdv{s}{x}{t}  \quad
\]
\[
\fdv{F}{g}
\]
\end{document}

enter image description here

edited Jan 29 '15 at 13:29

answered Jan 29 '15 at 13:18

4

Thank you very much for both answers! Both of them worked perfect. – David Jan 29 '15 at 13:24
I also tried the second option you gave, but when I had written \usepackage{physics} at the top of the document, I got this as an output: ! LaTeX Error: File `physics.sty' not found.
Type X to quit or to proceed, or enter new name. (Default extension: sty)

Enter file name:
– David Jan 29 '15 at 13:43
What should I enter as file name? – David Jan 29 '15 at 13:43
2

@David It means you don't have physics package installed. Please install it. – Jan 29 '15 at 13:57
Note that we can italicize the d's using \usepackage[italicdiff]{physics}. – Mateen Ulhaq Apr 09 '17 at 05:23
Thank you, I never know there was a physics package . – xue Nov 18 '22 at 23:10

Sebastiano · Answer 2 · 2024-02-09T12:13:01.860

18

Another possibility to write classic derivates or partial derivates I suggest (IMHO), actually, to use derivative package. For my humble opinion it is very good and last release is **2024/02/08, v1.4 **. Here there are some examples take, some, from the guide:

\documentclass[12pt]{article}
\usepackage{derivative}
\begin{document}
\[
\pdv{f}{x}, \quad \odv{Q}{t}=\odv{s}{t}, \quad \pdv{f}{x,y}, \quad 
\derivset{\odv}[switch-*=false] \odv{y}{x}, \quad \odv[n]{y}{x}, \quad
\derivset{\odv}[misc-add-delims=fun] \odv*{\odv{y}{x}}{x}, \quad 
\derivset{\pdv}[sort-method={sign,symbol,abs}] \pdv[c+kn,-b+2a]{f}{x,y}
\]
\end{document}

edited Feb 09 '24 at 12:13

answered Nov 08 '19 at 23:33

Sebastiano

54,118

1

Just fully agree IMHO with your HO: this package is very good. It is easy to use and has powerful options. +1 – loved.by.Jesus Jul 30 '21 at 10:13
@loved.by.Jesus I am help that you have appreciated my answer. + 1 also for you and other. – Sebastiano Jul 30 '21 at 10:28
What is the mnemonic for odv and pdv? I would guess "Ordinary Derivative..." and "Partial Derivative..." but what is the v standing for? – lucidbrot Mar 08 '22 at 10:41
1

@lucidbrot I got the naming scheme from another package, I think it was physics, but at least in my package dv stands for "DeriVative" or for short "DeriV". The latter is also the prefix for the internal package commands. – Simon Jun 28 '22 at 13:23

score 7 · Answer 3 · edited Jan 18 '17 at 20:37

7

I now recommend using the cool package:

\documentclass{article}
\usepackage{cool}
\begin{document}
Text:
\[
    \pderiv{u}{t}=\pderiv[2]{u}{x}
\]
More text.
\end{document}

I used to recommend defining a command to make a short form:

\documentclass{article}
% Partial derivative
\newcommand*{\pd}[3][]{\ensuremath{\frac{\partial^{#1} #2}{\partial #3}}}
\begin{document}
Text:
\[
    \pd{u}{t}=\pd[2]{u}{x^2}
\]
More text.
\end{document}

what it looks like

edited Jan 18 '17 at 20:37

CroCo

5,902

answered Jan 29 '15 at 13:28

Benjamin McKay

4,171

1

There is rarely a good use of \ensuremath. While there's nothing really wrong with it, it removes semantic meaning without adding much of anything else. See When not to use \ensuremath for math macro? – Paul Gessler Jan 29 '15 at 13:33
You do not have to make that square in denominator by hand... you can formulate it in this way: \newcommand{\pdv}[3][]{\frac{\partial^{#1}#2}{\partial {#3}^{#1}}} – Jozef Janočko Feb 19 '16 at 18:27
1

@JozefJanočko Note that \partial^{}u (the default in your solution) will give more spacing compared to \partial u. – sodd Feb 19 '16 at 21:18

score 2 · Answer 4 · answered Feb 01 '19 at 16:40

2

Try this

\frac{\partial^2 u}{\partial x^2}

answered Feb 01 '19 at 16:40

AGN

21

7

This doesn't add anything more than isn't already covered in the other answer(s). – Werner Feb 01 '19 at 19:51

score 2 · Answer 5 · answered Mar 09 '21 at 20:58

All good answers. I would just like to mention that if your are somewhat new to LaTeX, you should get used to using \newcommand and \renewcommand. For example:

% __________ Differentials __________

% Single

  \newcommand{\diff}{d}           % If you want an upright `d', change it here
  \newcommand{\p}[1]{\partial#1}
  \newcommand{\q}[1]{\delta#1}    % Kronecker Delta/Variation Symbol

% Nth Differentials:

  \newcommand{\dN}[2]{\diff^{#1}{#2}}   % Numerator type
  \newcommand{\pN}[2]{\partial^{#1}{#2}}
  \newcommand{\qN}[2]{\delta^{#1}{#2}}

% Nth Powers of Differentials

  \newcommand{\dD}[2]{\diff{#2}^{#1}}   % Denominator type
  \newcommand{\pD}[2]{\p{#2}^{#1}}
  \newcommand{\qD}[2]{\delta{#2}^{#1}}
  \newcommand{\pd}[1]{\dfrac{\partial}{\partial{#1}}}
  \newcommand{\pdd}[2]{\dfrac{\partial{#1}}{\partial{#2}}}

% __________ Derivatives __________

% 1st derivative:

\newcommand{\dod}[2]{\dfrac{\diff{#1}}{\diff{#2}}}  % 'differential over differential'
\newcommand{\pop}[2]{\dfrac{\p#1}{\p#2}}            % 'partial over partial'
\newcommand{\lpop}[2]{\p#1/\p#2}            % A 'layed down' version
\newcommand{\qoq}[2]{\dfrac{\q#1}{\q#2}}

% Nth derivative:

\newcommand{\dodN}[3]{\dfrac{\dN{#1}{#2}}{\dD{#1}{#3}}}
\newcommand{\popN}[3]{\dfrac{\pN{#1}{#2}}{\pD{#1}{#3}}}
\newcommand{\lpopN}[3]{\pN{#1}{#2}/\pD{#1}{#3}}  % Layed version of \pop
\newcommand{\qoqN}[3]{\dfrac{\qN{#1}{#2}}{\qD{#1}{#3}}}

% Mixed

\newcommand{\dodMixed}[3]{\dfrac{\dN{2}{#1}}{\diff{#2}\diff{#3}}}
\newcommand{\popMixed}[3]{\dfrac{\pN{2}{#1}}{\p{#2}\p{#3}}}
\newcommand{\lpopMixed}[3]{\pN{2}{#1}/\p{#2}\p{#3}}
\newcommand{\qoqMixed}[3]{\dfrac{\qN{2}{#1}}{\q{#2}\q{#3}}}

score 1 · Answer 6 · answered Feb 09 '24 at 12:22

Another option is to use hep-math package (2023/07/01). Here a little tex.code compilable.

\documentclass[12pt]{article}
\usepackage{hep-math}
\renewcommand{\diffsymbol}{\mathrm d} % optional upright d
\begin{document}
[\dv[f]x,\quad, \dv[f]x^n,\quad, \dv[f]x^n,\quad, \dv[f]x^n]
[\dv xf,\quad, \dvxf,\quad, \dv xf,\quad, \dvxf]
[\pdv[f]h,\quad, \pdv[f]y[x],\quad, \pdv[f]x^5,\quad, \pdv[f]x^3[y^2]]
[\pdv[f]x^2[y]^3, \pdv[f]x[y]^3, \pdv x[y]f]
\end{document}

+1 for bringing up a package I didn't know but I wouldn't recommend it... — campa, Feb 09 '24 at 14:17

How to write partial differential equation (Ex. dQ/dt=ds/dt) with real partial derivative signs?

6 Answers6