% !TEX program = pdfLaTeX
\documentclass{standalone}
\input{00_myPreamble.tex}
\input{00_myNewCommands.tex}
% ==== ==== ==== ====
\begin{document}
$\displaystyle
  \begin{pmatrix}
     x_1 \\ y_1 \\ z_1
  \end{pmatrix} = 
  \begin{pmatrix}
     x_0 \\ y_0 \\ z_0
  \end{pmatrix} - 
  \begin{pmatrix}
     \der{f}{x}{y,z} & \der{f}{y}{x,z} & \der{f}{z}{x,y} \\ 
     \der{g}{x}{y,z} & \der{g}{y}{x,z} & \der{g}{z}{x,y} \\
     \der{h}{x}{y,z} & \der{h}{y}{x,z} & \der{h}{z}{x,y} \\
  \end{pmatrix}^{-1}
  \begin{pmatrix}
     f(x_0,y_0,z_0) \\ g(x_0,y_0,z_0) \\ h(x_0,y_0,z_0)
  \end{pmatrix}
$
\end{document}