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<quiz>
  <question type="stack">
    <name>
      <text>CR-Diff-06-chain-1.d</text>
    </name>
    <questiontext format="html">
      <text>Differentiate {@p@} with respect to {@v@}.

[[input:ans1]] [[validation:ans1]]</text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[In order to solve this problem we will have to use the chain rule <hint>calc_chain_rule</hint> as follows:
 
Define \(f({@v@})={@p@}\) and \(g({@v@})={@pp@}\). 

So \(f({@v@})=g({@v@})^{@rdm3@}\). So, 

\[\begin{array}{rcl}\displaystyle 
  \frac{d}{d{@v@}}[{@p@}] &\displaystyle =&\displaystyle  \frac{df}{dg}\cdot \frac{dg}{d{@v@}} \\
   &\displaystyle =&\displaystyle  \frac{d}{dg}(g^{@rdm3@})\cdot \frac{d}{d{@v@}}({@pp@}) \\
   &\displaystyle =&\displaystyle  {@rdm3@}g^{{@rdm3@}-1}\cdot {@rdm2@} \\
   &\displaystyle =&\displaystyle  {@rdm3*rdm2@}({@pp@})^{@rdm3-1@} \\
   &\displaystyle =&\displaystyle  {@diff(p,v)@}
 \end{array}\]]]></text>
    </generalfeedback>
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    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>v:x;
rdm1:2+rand(7);
rdm2:2+rand(5);
rdm3:1/2;
pp:rdm1+rdm2*v;
p:(pp)^rdm3;</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:Result]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\[\frac{d}{d{@v@}}({@p@}) = {@diff(p,v)@} \]</text>
    </questionnote>
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      <text/>
    </questiondescription>
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    <prtcorrect format="html">
      <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>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
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    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>diff(p,v)</tans>
      <boxsize>15</boxsize>
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    </input>
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      <node>
        <name>0</name>
        <description/>
        <answertest>Diff</answertest>
        <sans>ans1</sans>
        <tans>diff(p,v)</tans>
        <testoptions>v</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
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      <node>
        <name>1</name>
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        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>diff(p,v)/diff(pp,v)</tans>
        <testoptions/>
        <quiet>0</quiet>
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        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-1-T </trueanswernote>
        <truefeedback format="html">
          <text>You need to use the chain rule so that \[\frac{d}{dx}[f(g(x))]=\frac{df}{dg}\cdot \frac{dg}{dx}\] but you have not included the \(\frac{dg}{dx}\) term.</text>
        </truefeedback>
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        <falseanswernote>Result-1-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
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        <value>ev(diff(p,v),simp)</value>
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    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(diff(p,v)/diff(pp,v),simp)</value>
      </testinput>
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        <name>Result</name>
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  </question>
</quiz>
