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