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salagne
2020-06-17 12:30:44 +02:00
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\documentclass{lecture}
\begin{document}
\newcommand{\pdv}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\dv}[2]{\frac{\d #1}{\d #2}}
\newcommand{\dv}[2]{\frac{\mathrm{d} #1}{\mathrm{d} #2}}
\section{Totale Differenzierbarkeit}
Erinnerung (Analysis 1) $f \colon D \to \R,\; D \subset \R$, ist genau dann in $x\in D$ differenzierbar, falls $f$ in $x$ ,,gut`` linear approximierbar ist, d.h. $\exists a\in \R$ mit $f(x + h) = f(x) + a\cdot h + w(h)$ wobei $\lim\limits_{h\to 0} \frac{w(h)}{|h|} = 0 \ (f'(x) = a)$.