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    <name>
      <text><![CDATA[11.2.1d diff trig & e & ln]]></text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>

<ol class="HELM_parts">
Find the derivative of each of the following with respect to the appropriate variable:<p></p>
<li><p></p><p></p>
\(\sin (-{@a1@}x)\)
<p></p><p>  [[input:ans1]]
 [[validation:ans1]][[feedback:prt1]]</p>

</li><li>
\(\cos \dfrac{ {@b1@}}{2}t\)
<p></p><p>[[input:ans2]]
 [[validation:ans2]][[feedback:prt2]]</p></li>

<li><p></p><p></p>
\(\tan \pi x\)
<p></p><p>  [[input:ans3]]
 [[validation:ans3]][[feedback:prt3]]</p>

</li><li>
\(e^{ \frac{x}{{@d1@}} }\)
<p></p><p>[[input:ans4]]
 [[validation:ans4]][[feedback:prt4]]</p></li>

<li><p></p><p></p>
\( \ln \dfrac{ {@e1@} }{3} t \)
<p></p><p>  [[input:ans5]]
 [[validation:ans5]][[feedback:prt5]]</p></li></ol>]]></text>
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      <text>2020081700</text>
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    <questionvariables>
      <text>a1:rand([5,7,9]);
ta1:diff(sin(-a1*x),x);

b1:rand([3,5]);
ta2:diff(cos(b1/2*t),t);

c1:rand([4,6,8]);
ta3:diff(tan(pi*x),x);

d1:rand([3,5]);
ta4:diff(e^(x/d1),x);

e1:rand([2,4,5]);
ta5:diff(ln(e1/3*t),t);</text>
    </questionvariables>
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    <questionnote format="moodle_auto_format">
      <text>\[ y= \sin (-{@a1@}x) \rightarrow y' = {@ta1@}, \quad y= \cos \dfrac{ {@b1@}}{2}t \rightarrow y' = {@ta2@}\]
\[ \quad y=\tan \pi x \rightarrow y' = {@ta3@}, \quad y=e^{ \frac{x}{{@d1@}} } \rightarrow y' ={@ta4@}, \quad y=\ln \dfrac{ {@e1@} }{3} t \rightarrow y' ={@ta5@} \]</text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
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    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
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          <text><![CDATA[<p>The derivative is \({@ta1@}\)</p>]]></text>
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          <text>The derivative is \({@ta2@}\)</text>
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          <text>The derivative is \({@ta3@}\)</text>
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