Partial derivative with respect to three variables

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} 

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}