Review Note
Last Update: 10/20/2024 08:27 AM
Current Deck: Mathematik::Analysis 2
Published
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Front
Satz: Diff'regeln auf \(\Omega\subset\mathbb{R}^n\)
Kettenregel, 1. Version: \(\mathbb{R}^n\overset{g}{\to}\mathbb{R}\overset{f}{\to}\mathbb{R}\)
\(g:\Omega\to \mathbb{R}\) in \(x_0\in\Omega\) diff'bar und
\(f:\mathbb{R}\to\mathbb{R}\) in \(g(x_0)\) diff'bar
=>?
Kettenregel, 1. Version: \(\mathbb{R}^n\overset{g}{\to}\mathbb{R}\overset{f}{\to}\mathbb{R}\)
\(g:\Omega\to \mathbb{R}\) in \(x_0\in\Omega\) diff'bar und
\(f:\mathbb{R}\to\mathbb{R}\) in \(g(x_0)\) diff'bar
=>?
Back
Funktion \((f\circ g):\Omega\to \mathbb{R}\) diff'bar in \(x_0\)
und es gilt:
\[d(f\circ g)(x_0)=f'(g(x_0))\,dg(x_0)\]
und es gilt:
\[d(f\circ g)(x_0)=f'(g(x_0))\,dg(x_0)\]
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