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<quiz>
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      <text>11.7.2 task</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Compute the derivative, \(\dfrac{dy}{dx}\) given \({@f@}={@g@}.\)</p><p>Note that your answer will be in terms of both \(y\) and \(x.\)</p><p>\( \dfrac{dy}{dx} =\) [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[We are given \({@f@}={@g@}.\)<br>By differentiating both sides of the equation, with respect to \(x\), and using the chain rule
on the \( \sin {@c@}y\) term, we get:
\[ \dfrac{d}{dx}({@f@}) = \dfrac{d}{dx}({@g@}) \]
so
\[ {@a@}\dfrac{dy}{dx} = {@b@}x^{ {@b-1@}} + {@c@} \cos ({@c@}y)\dfrac{dy}{dx} \]
which leads to
\[ \dfrac{dy}{dx} = \displaystyle{{@ta1@}}. \]]]></text>
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    <questionvariables>
      <text>a : rand(3)+2;
b : rand(5)+3;
c : rand(5)+3;

f : a*y ;
g : x^b + sin(c*y);
ta1 : b*x^(b-1)/(a - c*cos(c*y));</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
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    <questionnote format="moodle_auto_format">
      <text>\({@f@}={@g@}, \, \dfrac{dy}{dx} ={@ta1@}\)</text>
    </questionnote>
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      <text><![CDATA[<p><span class="partially">Your answer is partially correct.</span></p>]]></text>
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      <text><![CDATA[<p><span class="incorrect">Incorrect answer.</span></p>]]></text>
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