http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php?action=history&feed=atom&title=L%C3%B6sung_1.2%3A1e 2026-05-02T22:52:36Z Versionsgeschichte für diese Seite in Online Mathematik Brückenkurs 2 MediaWiki 1.11.1 http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php?title=L%C3%B6sung_1.2:1e&diff=4232&oldid=prev 2009-04-18T19:13:53Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 19:13, 18. Apr. 2009</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">The quotient rule gives</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Durch die Quotientenregel erhalten wir</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Abgesetzte Formel||&lt;math&gt;\begin{align}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Abgesetzte Formel||&lt;math&gt;\begin{align}</div></td></tr> </table>

Martin http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php?title=L%C3%B6sung_1.2:1e&diff=3530&oldid=prev 2009-03-11T10:02:55Z

<p><a href="/wikis/2009/bridgecourse2-TU-Berlin/index.php?title=Solution_1.2:1e&amp;action=edit" class="new" title="Solution 1.2:1e">Solution 1.2:1e</a> moved to <a href="/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_1.2:1e" title="Lösung 1.2:1e">Lösung 1.2:1e</a>: Robot: moved page</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 10:02, 11. Mär. 2009</td> </tr> </table>

Tekbot http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php?title=L%C3%B6sung_1.2:1e&diff=3015&oldid=prev 2009-03-10T12:52:34Z

<p>Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 12:52, 10. Mär. 2009</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The quotient rule gives</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The quotient rule gives</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">Displayed math</del>||&lt;math&gt;\begin{align}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{{<ins style="color: red; font-weight: bold; text-decoration: none;">Abgesetzte Formel</ins>||&lt;math&gt;\begin{align}</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\Bigl(\frac{x}{\ln x}\Bigr)'</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\Bigl(\frac{x}{\ln x}\Bigr)'</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&amp;= \frac{(x)'\cdot \ln x - x\cdot (\ln x)'}{(\ln x)^2}\\[5pt]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&amp;= \frac{(x)'\cdot \ln x - x\cdot (\ln x)'}{(\ln x)^2}\\[5pt]</div></td></tr> </table>

Tekbot http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php?title=L%C3%B6sung_1.2:1e&diff=2609&oldid=prev 2008-10-14T14:14:16Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 14:14, 14. Okt. 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The quotient rule gives</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The quotient rule gives</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">{{Displayed math||</ins>&lt;math&gt;\begin{align}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\begin{align}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\<ins style="color: red; font-weight: bold; text-decoration: none;">Bigl</ins>(\frac{x}{\ln x}\<ins style="color: red; font-weight: bold; text-decoration: none;">Bigr</ins>)<ins style="color: red; font-weight: bold; text-decoration: none;">'</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&amp; </del>\<del style="color: red; font-weight: bold; text-decoration: none;">left</del>( \frac{x}{\ln x} \<del style="color: red; font-weight: bold; text-decoration: none;">right</del>)<del style="color: red; font-weight: bold; text-decoration: none;">^{\prime }</del>=\frac{<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( x <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)<del style="color: red; font-weight: bold; text-decoration: none;">^{\prime }</del>\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\ln x-x\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot \left</del>( \ln x <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)<del style="color: red; font-weight: bold; text-decoration: none;">^{\prime }</del>}{<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( \ln x <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)^<del style="color: red; font-weight: bold; text-decoration: none;">{</del>2<del style="color: red; font-weight: bold; text-decoration: none;">}</del>} \\ </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= \frac{(x)<ins style="color: red; font-weight: bold; text-decoration: none;">'</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>\ln x - x\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>(\ln x)<ins style="color: red; font-weight: bold; text-decoration: none;">'</ins>}{(\ln x)^2}\\<ins style="color: red; font-weight: bold; text-decoration: none;">[5pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&amp; \\ </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&amp;= \frac{1\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\ln x - x\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">dfrac</ins>{1}{x}}{(\ln x)^2}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[5pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&amp; =\frac{1\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\ln x-x\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\<del style="color: red; font-weight: bold; text-decoration: none;">frac</del>{1}{x}}{<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( \ln x <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)^<del style="color: red; font-weight: bold; text-decoration: none;">{</del>2}<del style="color: red; font-weight: bold; text-decoration: none;">}</del>=\frac{\ln x-1}{<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( \ln x <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)^<del style="color: red; font-weight: bold; text-decoration: none;">{</del>2}<del style="color: red; font-weight: bold; text-decoration: none;">}</del>=\frac{1}{\ln x}-\frac{1}{<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( \ln x <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)^<del style="color: red; font-weight: bold; text-decoration: none;">{</del>2<del style="color: red; font-weight: bold; text-decoration: none;">}</del>} \\ </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= \frac{\ln x-1}{(\ln x)^2}<ins style="color: red; font-weight: bold; text-decoration: none;">\\[5pt]</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\end{align}&lt;/math&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp;</ins>= \frac{1}{\ln x} - \frac{1}{(\ln x)^2}\<ins style="color: red; font-weight: bold; text-decoration: none;">,</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">textrm{.}</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\end{align}&lt;/math&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">}}</ins></div></td></tr> </table>

Tek http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php?title=L%C3%B6sung_1.2:1e&diff=1615&oldid=prev 2008-09-16T14:23:21Z

<p><a href="/wikis/2009/bridgecourse2-TU-Berlin/index.php?title=L%C3%B6sning_1.2:1e&amp;action=edit" class="new" title="Lösning 1.2:1e">Lösning 1.2:1e</a> moved to <a href="/wikis/2009/bridgecourse2-TU-Berlin/index.php?title=Solution_1.2:1e&amp;action=edit" class="new" title="Solution 1.2:1e">Solution 1.2:1e</a>: Robot: moved page</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 14:23, 16. Sep. 2008</td> </tr> </table>

Tekbot http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php?title=L%C3%B6sung_1.2:1e&diff=1285&oldid=prev 2008-09-12T15:39:56Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 15:39, 12. Sep. 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_START</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The quotient rule gives</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&lt;center&gt; [[Image:1_2_1e.gif]] &lt;/center&gt;</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_STOP</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;\begin</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">align}</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp; \left( \frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">x</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">{\ln x</ins>} <ins style="color: red; font-weight: bold; text-decoration: none;">\right)^{\prime }=\frac{\left( x \right)^{\prime }\centerdot \ln x-x\centerdot \left( \ln x \right)^{\prime }}{\left( \ln x \right)^{2}} \\ </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp; \\ </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&amp; =\frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">1\centerdot \ln x-x\centerdot \frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">1</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">{x</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">}{\left( \ln x \right)^{2}}=\frac{\ln x-1}{\left( \ln x \right)^{2}}=\frac{1}{\ln x}-\frac{1}{\left( \ln x \right)^{2}} \\ </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">\end{align}&lt;/math&gt;</ins></div></td></tr> </table>

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<p>Robot: Automated text replacement (-[[Bild: +[[Image:)</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">← Nächstältere Version</td> <td colspan='2' style="background-color: white; color:black;">Version vom 07:51, 21. Aug. 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;center&gt; [[<del style="color: red; font-weight: bold; text-decoration: none;">Bild</del>:1_2_1e.gif]] &lt;/center&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;center&gt; [[<ins style="color: red; font-weight: bold; text-decoration: none;">Image</ins>:1_2_1e.gif]] &lt;/center&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td></tr> </table>

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