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@@ -75,7 +75,7 @@ Erinnerung (Analysis 1) $f \colon D \to \R,\; D \subset \R$, ist genau dann in $ |
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&= h'(0) |
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\intertext{Kettenregel:} |
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h'(t) &= \sum_{i = 1}^{n} \pdv{f}{x_i}(\xi(t))\cdot \xi_i'(t)\\ |
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\implies h'(0) &\stackrel{\xi(0) = x + 0\cdot v, \xi_i'(t) = v_i}{=} \sum_{i = 1}^{n}\pdv{f}{x_i}(x)\cdot v_i\\ |
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\implies h'(0) &\stackrel[\xi_i'(t) = v_i]{\xi(0) = x + 0\cdot v}{=} \sum_{i = 1}^{n}\pdv{f}{x_i}(x)\cdot v_i\\ |
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&= (\nabla f(x),v)_2 |
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\end{salign*} |
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\end{proof} |
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