Benutze besser `\setbeamertemplate{background canvas}{...}`. Du musst lediglich die Dimensionen des `grid` richtig einstellen:
`\setbeamertemplate{background canvas}{%
\begin{tikzpicture}
% optional:
\fill[color=orange!10] (0,0) rectangle (\paperwidth,\paperheight);
% kariert:
\draw[step=0.5,help lines] (0,0) grid (\paperwidth,\paperheight);
\end{tikzpicture}}
`
Funktioniert auch:
`\usebackgroundtemplate{\begin{tikzpicture}%
\draw[step=0.5,help lines] (0,0) grid (\paperwidth,\paperheight);
\end{tikzpicture}}`
[![alt text][3]][3]
\documentclass{beamer}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage{amsmath}
\usepackage{tikz}
\begin{document}
% Alt:
%\usebackgroundtemplate{\begin{tikzpicture}%
% \draw[step=.5,yshift=-1cm] (0,0) grid (13,10);%
% \draw[fill=white](0,10) rectangle (13,9);%
% \draw[fill=black] (0.75,8.25) circle(1pt);%
% %\draw[fill=blue] (0.75,8.25) circle(1pt) node[right]{Definitionsbereich};
%\end{tikzpicture}}
% Neu:
\setbeamertemplate{background canvas}{%
\begin{tikzpicture}
% optional:
\fill[color=orange!10] (0,0) rectangle (\paperwidth,\paperheight);
% kariert:
\draw[step=0.5,help lines] (0,0) grid (\paperwidth,\paperheight);
\end{tikzpicture}}
\begin{frame}{$f:D\rightarrow\mathbb R,~x\mapsto\frac{1}{x}$}
\begin{itemize}
\item Definitionsbereich
\end{itemize}
\end{frame}
\end{document}
[3]: https://texwelt.de/wissen/upfiles/55555555_138.png
