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}