https://peda.net/id/ffe0db68ce9 2025-12-01T10:52:00+02:00 https://peda.net/:static/539/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/4f7e0c50ceb 2025-12-01T17:32:30+02:00 <br/> Derivaatta h(x)=ln(((x^(2)-1)/(x^(2)+1)))<br/> <br/> Derivata di una funzione composta: 𝑦=𝑔⁡[𝑓⁡(𝑥)]→𝑦′= l′⁡[𝑓⁡(𝑥)]⋅𝑓′⁡(𝑥)<br/> <br/>  l⁡(𝑥)=ln⁡𝑥  → l′⁡(𝑥)= 1 / 𝑥<br/> <br/> f(x)=((x^(2)-1)/(x^(2)+1)) <br/> <br/> 𝑦= 𝑓⁡(𝑥) / 𝑔⁡(𝑥)  → 𝑦′= (𝑓′⁡(𝑥)⋅𝑔⁡(𝑥)−𝑓⁡(𝑥)⋅𝑔′⁡(𝑥)) / [𝑔⁡(𝑥)]2<br/> <br/> f'(x)=[(2x⋅(x^2 +1) - (2x⋅(x^2 -1)] / (x^2+1)^2 = [ (2x⋅(x^2 +1) - (2x⋅(x^2 -1) ] / (x^4+ 2x^2 +1) <br/> <br/> Ratkaisu:<br/> <a href="https://www.geogebra.org/calculator/rntxeegu" rel="noopener nofollow ugc" target="_blank">https://www.geogebra.org/calculator/rntxeegu</a><br/> <br/> <br/> <table border="1" style="border-collapse: collapse; width: 100%;"> <tbody> <tr> <td> <div class="container"> <div class="main"><br/> <h2>Derivaattojen harjoitukset ja ratkaisut 1-15:</h2> <hr></hr> <div class="flex-container"> <div> <h2>Harjoitus 1</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x1.png"/><!--filtered attribute: border="0"--></p> </div> <div id="adv"> </div> <div> <h2>Harjoitus 2</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x2.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 3</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x3.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 4</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x4.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 5</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x5.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 6</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x6.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 7</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x7.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 8</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x8.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 9</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x9.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 10</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x10.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 11</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x11.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 12</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x12.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 13</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x13.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 14</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x14.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 15</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x15.png"/><!--filtered attribute: border="0"--></p> </div> <div> </div> <div> <p> </p> </div> </div> </div> </div> <div id="r89-desktop-billboard-low-0-wrapper"> <div id="r89-desktop-billboard-low-0"> </div> </div> </td> <td> <div class="container"> <div class="main"><br/> <h2>Derivaattojen harjoitukset ja ratkaisut 16-30:</h2> <hr></hr> <div> <h2>Harjoitus 16</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x16.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 17</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x17.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 18</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x18.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 19</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x19.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 20</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x20.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 21</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x21.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 22</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x22.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 23</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x23.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 24</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x24.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 25</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x25.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 26</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x26.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 27</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x27.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 28</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x28.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 29</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x29.png"/><!--filtered attribute: border="0"--></p> </div> <div> <h2>Harjoitus 30</h2> <p><img src="https://www.edutecnica.it/matematica/derivatex/x30.png"/><!--filtered attribute: border="0"--></p> </div> </div> </div> </td> </tr> <tr> <td> <ul> <li><a href="https://www.edutecnica.it/matematica/derivate/derivate.htm" rel="nofollow ugc noopener">Teoria</a><a href="https://www.edutecnica.it/math.htm" rel="nofollow ugc noopener"></a></li> </ul> </td> <td> <ul> <li><a href="https://www.edutecnica.it/matematica/derivate/derivate.htm" rel="nofollow ugc noopener">Matematica</a><a href="https://www.edutecnica.it" rel="nofollow ugc noopener"></a></li> </ul> </td> </tr> <tr> <td>- <a href="https://www.edutecnica.it/matematica/derivatex/derivatex.htm" rel="noopener nofollow ugc" target="_blank">Derivaattojen harjoitukset ja ratkaisut</a> :</td> <td><a href="https://www.edutecnica.it/matematica/derivatex/derivatex.htm" rel="nofollow ugc noopener">https://www.edutecnica.it/matematica/derivatex/derivatex.htm</a></td> </tr> </tbody> </table> 2025-12-01T16:09:11+02:00 https://peda.net/id/d9ebad48cea 2025-12-01T12:38:18+02:00 <h1>Johdatus korkeakoulumatematiikkaan</h1> <br/> <a rel="noopener" target="_blank"><!--filtered attribute: 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