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Bevis for derivasjon av tan(x) - Sideversjonshistorikk
2026-04-09T01:51:28Z
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Administrator på 29. sep. 2017 kl. 09:45
2017-09-29T09:45:03Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Sideversjonen fra 29. sep. 2017 kl. 09:45</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Vi kan erstatte telleren i den siste brøken med 1 og får da: $(tan(x))' = \frac{1}{cos^2(x)}$</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Vi kan erstatte telleren i den siste brøken med 1 og får da: $(tan(x))' = \frac{1}{cos^2(x)}$</div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Derivasjonsregler ]]</ins></div></td></tr>
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Administrator på 29. sep. 2017 kl. 09:39
2017-09-29T09:39:56Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Eldre sideversjon</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Sideversjonen fra 29. sep. 2017 kl. 09:39</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$tan(x)= \frac{sin(x)}{cos(x)} $</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$tan(x)= \frac{sin(x)}{cos(x)} $</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$tan<del style="font-weight: bold; text-decoration: none;">'</del>(x)= ( \frac{sin(x)}{cos(x)})' \\ = \frac{sin(x) \cdot sin(x) - (-cos(x) \cdot cos(x))}{cos^2(x)} \\ = \frac{sin^2(x) + cos^2(x)}{cos^2(x)} \\= tan^2(x) + 1 $</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$<ins style="font-weight: bold; text-decoration: none;">(</ins>tan(x)<ins style="font-weight: bold; text-decoration: none;">)' </ins>= ( \frac{sin(x)}{cos(x)})' \\ = \frac{sin(x) \cdot sin(x) - (-cos(x) \cdot cos(x))}{cos^2(x)} \\ = \frac{sin^2(x) + cos^2(x)}{cos^2(x)} \\= tan^2(x) + 1 <ins style="font-weight: bold; text-decoration: none;">$</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Eventuelt har vi at $cos^2(x) + sin^2(x) = 1$ </ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Vi kan erstatte telleren i den siste brøken med 1 og får da: $(tan(x))' = \frac{1}{cos^2(x)}</ins>$</div></td></tr>
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Administrator på 29. sep. 2017 kl. 09:35
2017-09-29T09:35:56Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Eldre sideversjon</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Sideversjonen fra 29. sep. 2017 kl. 09:35</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$tan(x)= \frac{sin(x)}{cos(x)} $</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$tan(x)= \frac{sin(x)}{cos(x)} $</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>$tan'(x)= ( \frac{sin(x)}{cos(x)})' \\ = \frac{sin(x) \cdot sin(x) - (-cos(x) \cdot cos(x)}{cos^2(x)} $</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>$tan'(x)= ( \frac{sin(x)}{cos(x)})' \\ = \frac{sin(x) \cdot sin(x) - (-cos(x) \cdot cos<ins style="font-weight: bold; text-decoration: none;">(x))}{cos^2</ins>(x)} <ins style="font-weight: bold; text-decoration: none;">\\ = \frac</ins>{<ins style="font-weight: bold; text-decoration: none;">sin^2(x) + </ins>cos^2(x)}<ins style="font-weight: bold; text-decoration: none;">{cos^2(x)} \\= tan^2(x) + 1 </ins>$</div></td></tr>
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Administrator: Ny side: Vi har: $tan(x)= \frac{sin(x)}{cos(x)} $ $tan'(x)= ( \frac{sin(x)}{cos(x)})' \\ = \frac{sin(x) \cdot sin(x) - (-cos(x) \cdot cos(x)}{cos^2(x)} $
2017-09-29T09:34:05Z
<p>Ny side: Vi har: $tan(x)= \frac{sin(x)}{cos(x)} $ $tan'(x)= ( \frac{sin(x)}{cos(x)})' \\ = \frac{sin(x) \cdot sin(x) - (-cos(x) \cdot cos(x)}{cos^2(x)} $</p>
<p><b>Ny side</b></p><div><br />
Vi har:<br />
<br />
$tan(x)= \frac{sin(x)}{cos(x)} $<br />
<br />
$tan'(x)= ( \frac{sin(x)}{cos(x)})' \\ = \frac{sin(x) \cdot sin(x) - (-cos(x) \cdot cos(x)}{cos^2(x)} $</div>
Administrator