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      <text>11.2.1.1 Table of derivatives</text>
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      <text><![CDATA[<h4>Table of derivatives</h4>

The table below lists some of the common functions used in engineering and their corresponding derivatives. Remember that in each case the function in the right-hand column gives the rate of change, or the gradient of the graph, of the function on the left at a particular value of \(x\).
<p></p>
N.B. The angle must always be in radians when differentiating trigonometric functions.

<table class="HELM_table">
  <thead>
    <tr>
      <th>Function</th>
      <th>Derivative</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>constant</td>
      <td>0</td>
    </tr>
    <tr>
      <td>\(x\)</td>
      <td>\(1\)</td>
    </tr>
    <tr>
      <td>\(kx\)</td>
      <td>\(k\)</td>
    </tr>
    <tr>
      <td>\(x^n\)</td>
      <td>\(nx^{n-1}\)</td>
    </tr>
    <tr>
      <td>\(kx^n\)</td>
      <td>\(knx^{n-1}\)</td>
    </tr>
    <tr>
      <td>\(e^x\)</td>
      <td>\(e^x\)</td>
    </tr>
    <tr>
      <td>\(e^{kx}\)</td>
      <td>\(ke^{kx}\)</td>
    </tr>
    <tr>
      <td>\(\ln x\)</td>
      <td>\(1/x\)</td>
    </tr>
    <tr>
      <td>\(\ln kx\)</td>
      <td>\(1/x\)</td>
    </tr>
    <tr>
      <td>\(\sin x\)</td>
      <td>\(\cos x\)</td>
    </tr>
    <tr>
      <td>\(\sin kx\)</td>
      <td>\(k \cos kx\)</td>
    </tr>
      <tr><td>\(\sin (kx + c)\)</td>
      <td>\(k \cos (kx + c) \)</td>
    </tr>
      <tr><td>\(\cos x\)</td>
      <td>\(-\sin x\)</td>
    </tr>
    <tr>
      <td>\(\cos kx\)</td>
      <td>\(-k \sin kx\)</td>
    </tr>
      <tr><td>\(\cos (kx + c)\)</td>
      <td>\(-k \sin (kx + c) \)</td>
    </tr>
      <tr><td>\(\tan x\)</td>
      <td>\(\sec^2 x\)</td>
    </tr>
    <tr>
      <td>\(\tan kx\)</td>
      <td>\(k \sec^2 kx\)</td>
    </tr>
      <tr><td>\(\tan (kx + c)\)</td>
      <td>\(k \sec^2 (kx + c) \)</td>
    </tr>
  </tbody>
</table>]]></text>
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