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    <name>
      <text>11.4.2.7 1e quotient rule</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
Find the derivative of \(y = \displaystyle{{@y(x)@}}\) using the quotient rule.<p></p><p>We can see that the two functions are&nbsp;</p><p>\[ f(x) = {@f(x)@} \hspace{1cm} g(x) = {@g(x)@} \]</p><p>Now find the derivative of each of these functions&nbsp;</p><p>\( \dfrac{df}{dx} = \) [[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p><p>\( \dfrac{dg}{dx} = \) [[input:ans2]] [[validation:ans2]][[feedback:prt2]]</p><p>Finally, we have&nbsp;</p><p>\( \dfrac{dy}{dx} = \)&nbsp;[[input:ans3]] [[validation:ans3]][[feedback:prt3]]</p><p><br></p><p><br></p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We have \(y = \dfrac{f(x)}{g(x)}\), with \( f(x) = {@f(x)@}\) and \(g(x) = {@g(x)@} \).</p>
<p>Then, \( \dfrac{df}{dx} = {@ta1@} \) and \( \dfrac{dg}{dx} = \displaystyle{{@ta2@}}\).</p>
<p>So \[\begin{align*} \dfrac{dy}{dx} &amp;= \dfrac{ ({@g(x)@})(\displaystyle{{@ta1@}}) - \displaystyle{({@ta2@})}({@f(x)@})} {{@g(x)^2@}} \\ &amp;= \displaystyle{{@ta3@}}. \end{align*}\]
</p>]]></text>
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    <idnumber/>
    <stackversion>
      <text>2021120900</text>
    </stackversion>
    <questionvariables>
      <text>a:rand([2,3,4]);
b:2*a;
f(x):=sinh(a*x);
g(x):=cos(b*x);
y(x):=f(x)/g(x)
ta1:diff(f(x),x);
ta2:diff(g(x),x);
ta3:diff(y(x),x);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[ y = {@y(x)@}, y' = {@ta3@} \]</text>
    </questionnote>
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      <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>
    </prtcorrect>
    <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>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
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