# Partial derivative with respect to three variables

I just started learning LaTeX and I am facing problem in writing the following equation, can anyone please help me out?

A simpler code with the diffcoeff package. The order of differentiation is automatically computed — I suppose k+l is k_1+k_2+l:

\documentclass{article}
\usepackage{mathtools, diffcoeff}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}

\begin{document}

$\abs*{\diffp[k_1,k_2,l]{u_0} {x_1, x_2, t}} \leq C$

\end{document}


• I didn't know about diffcoeff. Nice. Off topic: k_1+k_2+l just to be compatible with order of powers in denominator? :-) – Sigur Feb 22 at 14:09
• @Sigur: it is a comparatively recent package. For the question: yes it is so. Of course, I understand that probably, $k$ denotes $k_1+k_2$, but there doesn't seem to be tools to use k in the numerator and k_1, k_2 in the denominator. – Bernard Feb 22 at 14:15
• Is there any way to eliminate the parentheses around the variables in the denominator? IMHO, adding parentheses like this creates ambiguity and is wrong. See i.stack.imgur.com/Jc3v8.png The powers k_1, k_2 and l should be applied to the whole \partial <variable> thing. – Ruixi Zhang Feb 23 at 13:05
• It seems to be hard-coded in the package for so-called long variables (it goes into the category, I suspect, because of the indices). As it's written in latex 3, which I don't master, I have no idea how to patch it, unfortunately. Maybe, ask a new question about this feature? – Bernard Feb 23 at 13:54

You could write

$\left\lvert\frac{\partial^{k+l}u_0} {{\partial x_1}^{k_1}{\partial x_2}^{k_2}\partial t^l}\right\rvert \leq C$


one more variation ...

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}

\begin{document}
$\abs*{\frac{\partial^{k+l}u_0} {\partial x_1^{k_1}\partial x_2^{k_2}\partial t^l}} \leq C$
\end{document}


• How did you produce the frame around the image? – Sigur Feb 22 at 13:55
• @Sigur, it is not part of latex code, but drawn by Snipping Tool, which i use for copping image from pdf previewer to site. in it i select option Show Ink selection ... – Zarko Feb 22 at 14:01
• Ah, OK. I use Shutter. Maybe there is such frame option there. – Sigur Feb 22 at 14:02
• Thanks to you I've just created a plugin for Shutter to add 1px solid blue frame around the image. Now I need to know how to run it automatically when screen shot is created. – Sigur Feb 22 at 15:03
• For the frame around formula in LaTeX, simply use \boxed{...} inside the math context. Of course, to get the wide white horizontal margin you would have to manually add some space with \hspace or \qquad – Jhor Feb 22 at 20:55

Like this?

\documentclass{report}
\usepackage{amsmath}

\begin{document}
$\Biggl\vert \frac{\partial^{k+l}u_0} {\partial^{k_1}{x_1}\, \partial^{k_2}{x_2}\, \partial^{l}{t}} \Biggr\vert \leq C,$
\end{document}

• The notation here is wrong I’m afraid. The k_1, k_2 and l should follow the variables, not the \partial signs. See i.stack.imgur.com/Jc3v8.png – Ruixi Zhang Feb 23 at 13:04
\documentclass{article}

\begin{document}
$\left | \frac{\partial^{k+1}u_0}{{\partial x_1}^{k_1} {\partial x_2}^{k_2} \partial t^l} \right | \leq C$
\end{document}


The first answer above suggested using the diffcoeff package, but the placing of parentheses around the variables in the denominator was questioned and also the exact form of the order of differentiation in the numerator. Both are easily changed or specified in diffcoeff:

\documentclass{article}
\usepackage{mathtools, diffcoeff}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\begin{document}

\diffdef{p}{long-var-wrap=dv}
$\abs*{\diffp[k_1,k_2,l][k+l]{u_0} {x_1, x_2, t}} \leq C$
\diffdef{p}{long-var-wrap=(dv)}
$\abs*{\diffp[k_1,k_2,l][k+l]{u_0} {x_1, x_2, t}} \leq C$
\end{document}


The second optional argument, [k+l] in this case, allows the automatically calculated and presented order of differentiation to be overwritten. The \diffdef command allows variant forms of derivative to be specified be means of a key=value list, the {p} indicating it is for partial derivatives in this case. The long-var-wrap key can take the values dv, d(v) the default, and (dv), depending on where you want to place the parentheses, if any. (I settled on d(v) as default after checking a small sample of texts. Although not strictly logical, it seemed a more common usage than either of the other possibilities.)