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201.216.11.230: /* Derivada de un cociente de funciones */
2013-04-11T19:46:39Z
<p><span class="autocomment">Derivada de un cociente de funciones</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 19:46 11 abr 2013</td>
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<tr><td colspan="2" class="diff-lineno">Línea 184:</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \, \frac{x^2}{e^x} \,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \, \frac{x^2}{e^x} \,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>^\prime \, = \, \frac{\left( \, x^2 \, \right)^\prime \cdot e^x - x^2\cdot\left(</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>^\prime \, = \, \frac{\left( \, x^2 \, \right)^\prime \cdot e^x - x^2\cdot\left(, e^x \, \right)^2} =</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;"> \, e^x \, \right)^\prime}{\left( \</del>, e^x \, \right)^2} =</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \frac{2x \cdot e^x - x^2 \cdot e^x }{e^{2x}} = \frac{2x - x^2}{e^x} </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div> \frac{2x \cdot e^x - x^2 \cdot e^x }{e^{2x}} = \frac{2x - x^2}{e^x} </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
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201.216.11.230
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201.215.98.105: /* Derivada una función constante */
2013-04-09T23:19:59Z
<p><span class="autocomment">Derivada una función constante</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 23:19 9 abr 2013</td>
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<tr><td colspan="2" class="diff-lineno">Línea 17:</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Si &nbsp;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Si &nbsp;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\mathrm{f} \left( \, x \, \right) = <del style="color: red; font-weight: bold; text-decoration: none;">2</del>, \, \forall x \in \mathbb{R}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\mathrm{f} \left( \, x \, \right) = <ins style="color: red; font-weight: bold; text-decoration: none;">1</ins>, \, \forall x \in \mathbb{R}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math>,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math>,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&nbsp; entonces</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&nbsp; entonces</div></td></tr>
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201.215.98.105
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Jvillalva en 15:26 19 abr 2012
2012-04-19T15:26:56Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 15:26 19 abr 2012</td>
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<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>==Derivada <del style="color: red; font-weight: bold; text-decoration: none;">de un Mamañema</del>==</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>==Derivada <ins style="color: red; font-weight: bold; text-decoration: none;">una función constante</ins>==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f} \left( \, x \, \right) = 2, \, \forall x \in \mathbb{R}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f} \left( \, x \, \right) = 2, \, \forall x \in \mathbb{R}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math>,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math>,</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; <del style="color: red; font-weight: bold; text-decoration: none;">Buen Mamaguevo</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; <ins style="color: red; font-weight: bold; text-decoration: none;">entonces</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\mathrm{f}^\prime \left( \, <del style="color: red; font-weight: bold; text-decoration: none;">Tu Puta Madre </del>\, \right) = 0, \, \forall x \in \mathbb{R}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\mathrm{f}^\prime \left( \, <ins style="color: red; font-weight: bold; text-decoration: none;">x </ins>\, \right) = 0, \, \forall x \in \mathbb{R}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
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Jvillalva
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190.167.40.65: /* Derivada una función constante */
2012-04-18T13:17:35Z
<p><span class="autocomment">Derivada una función constante</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 13:17 18 abr 2012</td>
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<tr><td colspan="2" class="diff-lineno">Línea 3:</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></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>==Derivada <del style="color: red; font-weight: bold; text-decoration: none;">una función constante</del>==</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>==Derivada <ins style="color: red; font-weight: bold; text-decoration: none;">de un Mamañema</ins>==</div></td></tr>
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190.167.40.65
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190.167.40.65: /* Ejemplo */
2012-04-18T13:16:12Z
<p><span class="autocomment">Ejemplo</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 13:16 18 abr 2012</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f} \left( \, x \, \right) = 2, \, \forall x \in \mathbb{R}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f} \left( \, x \, \right) = 2, \, \forall x \in \mathbb{R}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math>,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math>,</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&nbsp; <del style="color: red; font-weight: bold; text-decoration: none;">entonces</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&nbsp; <ins style="color: red; font-weight: bold; text-decoration: none;">Buen Mamaguevo</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\mathrm{f}^\prime \left( \, <del style="color: red; font-weight: bold; text-decoration: none;">x </del>\, \right) = 0, \, \forall x \in \mathbb{R}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\mathrm{f}^\prime \left( \, <ins style="color: red; font-weight: bold; text-decoration: none;">Tu Puta Madre </ins>\, \right) = 0, \, \forall x \in \mathbb{R}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></center></div></td></tr>
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190.167.40.65
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Fjmolina en 18:41 2 ene 2011
2011-01-02T18:41:11Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 18:41 2 ene 2011</td>
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<tr><td colspan="2" class="diff-lineno">Línea 54:</td>
<td colspan="2" class="diff-lineno">Línea 54:</td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><center></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><math></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\left( \, \mathrm{f}_1 + \mathrm{f}_n + \ldots + \mathrm{f}_n \, \right) =</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\left( \, \mathrm{f}_1 + \mathrm{f}_n + \ldots + \mathrm{f}_n \, \right)<ins style="color: red; font-weight: bold; text-decoration: none;">^\prime </ins>=</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f}_1^\prime + \mathrm{f}_n^\prime + \ldots + \mathrm{f}_n^\prime</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f}_1^\prime + \mathrm{f}_n^\prime + \ldots + \mathrm{f}_n^\prime</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
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Fjmolina
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Fjmolina en 18:39 2 ene 2011
2011-01-02T18:39:24Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revisión de 18:39 2 ene 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><br/></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 colspan="2"> </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;"><center></ins></div></td></tr>
<tr><td colspan="2"> </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;"><math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left( \, \mathrm{f}_1 + \mathrm{f}_n + \ldots + \mathrm{f}_n \, \right) =</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left( \, \mathrm{f}_1 + \mathrm{f}_n + \ldots + \mathrm{f}_n \, \right) =</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f}_1^\prime + \mathrm{f}_n^\prime + \ldots + \mathrm{f}_n^\prime</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\mathrm{f}_1^\prime + \mathrm{f}_n^\prime + \ldots + \mathrm{f}_n^\prime</div></td></tr>
<tr><td colspan="2"> </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;"></math></ins></div></td></tr>
<tr><td colspan="2"> </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;"></center></ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\left(</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> \, x^2 <del style="color: red; font-weight: bold; text-decoration: none;">+ </del>x \,</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> \, x^2 <ins style="color: red; font-weight: bold; text-decoration: none;">- </ins>x \,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)^\prime =</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>\right)^\prime =</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>\left( \, x^2 \, \right)^\prime <del style="color: red; font-weight: bold; text-decoration: none;">+ </del>\left( \, x \, \right)^\prime = 2x <del style="color: red; font-weight: bold; text-decoration: none;">+ </del>1</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>\left( \, x^2 \, \right)^\prime <ins style="color: red; font-weight: bold; text-decoration: none;">- </ins>\left( \, x \, \right)^\prime = 2x <ins style="color: red; font-weight: bold; text-decoration: none;">- </ins>1</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></center></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></center></div></td></tr>
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Fjmolina
http://wikillerato.org/index.php?title=Propiedades_de_las_derivadas&diff=20450&oldid=prev
Fjmolina: Página nueva: __TOC__ <br/> ==Derivada una función constante== <br/> La derivada de una función constante es cero. <br/> ===Ejemplo=== <br/> Si <math> \mathrm{f} \left( \, x \, \r...
2011-01-02T18:37:10Z
<p>Página nueva: __TOC__ <br/> ==Derivada una función constante== <br/> La derivada de una función constante es cero. <br/> ===Ejemplo=== <br/> Si &nbsp; <math> \mathrm{f} \left( \, x \, \r...</p>
<p><b>Página nueva</b></p><div>__TOC__<br />
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==Derivada una función constante==<br />
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La derivada de una función constante es cero.<br />
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===Ejemplo===<br />
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Si &nbsp;<br />
<math><br />
\mathrm{f} \left( \, x \, \right) = 2, \, \forall x \in \mathbb{R}<br />
</math>,<br />
&nbsp; entonces<br />
<center><br />
<math><br />
\mathrm{f}^\prime \left( \, x \, \right) = 0, \, \forall x \in \mathbb{R}<br />
</math><br />
</center><br />
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==Derivada de una suma de funciones==<br />
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La [[Función derivada y derivadas sucesivas|derivada]] de la suma de dos funciones es<br />
igual a la suma de las derivadas de dichas funciones:<br />
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<center><br />
<math><br />
\left(<br />
\, \mathrm{f} \, + \, \mathrm{g} \,<br />
\right)<br />
^\prime \, = \, \mathrm{f}^\prime \, + \, \mathrm{g}^\prime \,<br />
</math><br />
</center><br />
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Este resultado, se puede ampliar a cualquier número de funciones:<br />
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\left( \, \mathrm{f}_1 + \mathrm{f}_n + \ldots + \mathrm{f}_n \, \right) =<br />
\mathrm{f}_1^\prime + \mathrm{f}_n^\prime + \ldots + \mathrm{f}_n^\prime<br />
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==Derivada de una diferencia de funciones==<br />
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La [[Función derivada y derivadas sucesivas|derivada]] de la diferencia de dos funciones es<br />
igual a la diferencia de las derivadas de dichas funciones:<br />
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<center><br />
<math><br />
\left(<br />
\, \mathrm{f} \, - \, \mathrm{g} \,<br />
\right)<br />
^\prime \, = \, \mathrm{f}^\prime \, - \, \mathrm{g}^\prime \,<br />
</math><br />
</center><br />
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===Ejemplo===<br />
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<center><br />
<math><br />
\left(<br />
\, x^2 + x \,<br />
\right)^\prime =<br />
\left( \, x^2 \, \right)^\prime + \left( \, x \, \right)^\prime = 2x + 1<br />
</math><br />
</center><br />
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==Derivada de un producto de funciones==<br />
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La [[Función derivada y derivadas sucesivas|derivada]] del producto de dos funciones,<br />
&nbsp;<br />
<math><br />
\mathrm{f}<br />
</math><br />
&nbsp; y &nbsp;<br />
<math><br />
\mathrm{g}<br />
</math><br />
, viene dada por la fórmula:<br />
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<center><br />
<math><br />
\left(<br />
\, \mathrm{f} \cdot \mathrm{g} \,<br />
\right)<br />
^\prime \, = \, \mathrm{f}^\prime \cdot \mathrm{g} \, + \, \mathrm{f} \cdot \mathrm{g}^\prime \,<br />
</math><br />
</center><br />
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===Ejemplo===<br />
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<center><br />
<math><br />
\left(<br />
\, x^2 \cdot x \,<br />
\right)^\prime =<br />
\left( \, x^2 \, \right)^\prime \cdot x + x^2 \cdot \left( \, x \,<br />
\right)^\prime = 2x \cdot x + x^2 \cdot 1 = 3x^2<br />
</math><br />
</center><br />
Observese que &nbsp;<br />
<math><br />
x^2 \cdot x = x^3<br />
</math><br />
&nbsp; y que la derivada de &nbsp;<br />
<math><br />
x^3<br />
</math><br />
&nbsp; es precisamente &nbsp;<br />
<math><br />
3x^2<br />
</math>.<br />
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==Derivada de un cociente de funciones==<br />
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La [[Función derivada y derivadas sucesivas|derivada]] del cociente &nbsp;<br />
<math><br />
\frac{f}{g}<br />
</math><br />
&nbsp; viene dada por la fórmula:<br />
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<br/><br />
<br />
<center><br />
<math><br />
\left(<br />
\, \frac{f}{g} \,<br />
\right)<br />
^\prime \, = \, \frac{\mathrm{f}^\prime \cdot \mathrm{g} \, - \, \mathrm{f} \cdot \mathrm{g}^\prime}{\mathrm{g}^2}<br />
</math><br />
</center><br />
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===Ejemplo===<br />
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<center><br />
<math><br />
\left(<br />
\, \frac{x^2}{e^x} \,<br />
\right)<br />
^\prime \, = \, \frac{\left( \, x^2 \, \right)^\prime \cdot e^x - x^2\cdot\left(<br />
\, e^x \, \right)^\prime}{\left( \, e^x \, \right)^2} =<br />
\frac{2x \cdot e^x - x^2 \cdot e^x }{e^{2x}} = \frac{2x - x^2}{e^x} <br />
</math><br />
</center><br />
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[[Category:Matemáticas]]</div>
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