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