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\begin{omgroup}[id=sec.differentiable]{Differentiable Functions}
\begin{module}[id=differentiable]
\importmodule[continuous]{continuous}
\symdef{difffunctions}[2]{\mathcal{C}^1(#1,#2)}
\abbrdef{DiffRR}[2]{\difffunctions\RealNumbers\RealNumbers}
\begin{definition}
A function $\fun{f}\RealNumbers\RealNumbers$ is called {\defi{differentiable}} at
$\inset{x}\RealNumbers$, iff for all $\epsilon>0$ there is a $\delta>0$, such that
$\rfrac{\absval{f(x)-f(y)}}{\absval{x-y}}<\epsilon$ for all $\absval{x-y}<\delta$.
\end{definition}
\end{module}
\end{omgroup}
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