# 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

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

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
\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} 