<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>CR-Diff-09-misc-3.e</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Find the following derivative: \[ \frac{d}{d{@v@}}\left[ {@p@}\right]. \] [[input:ans1]] [[validation:ans1]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>To solve this problem you will need to use the product rule calc_product_rule and the chain rulecalc_chain_rule. Let \(g({@v@})={@p2@}\) and \(f({@v@})=g({@v@})^{@rdm1@}\). Then, by the chain rule: \[\frac{d}{d{@v@}}\left[{@p@}\right] = \frac{df}{dg}\cdot\frac{dg}{d{@v@}}.\] In order to calculate \(\frac{dg}{d{@v@}}\) you need to use the product rule, by defining two new functions: \(h({@v@})={@v@}\) and \(i({@v@})={@p1@}\) so that \(g({@v@})=h({@v@})i({@v@})\). So, \[\begin{array}{rcl}\displaystyle \frac{d}{d{@v@}}[{@p2@}] &amp;\displaystyle =&amp;\displaystyle \frac{dh}{d{@v@}}\cdot i + h\cdot \frac{di}{d{@v@}}\\ &amp;\displaystyle =&amp;\displaystyle [{@diff(v,v)@}]{@p1@} + {@v@}[{@diff(p1,v)@}] \\ &amp;\displaystyle =&amp;\displaystyle {@diff(p2,v)@} \end{array}\] Hence, \[\begin{array}{rcl}\displaystyle \frac{d}{d{@v@}}\left[{@p@}\right] &amp;\displaystyle =&amp;\displaystyle \frac{df}{dg}\cdot\frac{dg}{d{@v@}} \\ &amp;\displaystyle =&amp;\displaystyle {@rdm1*p2^(rdm1-1)@} \cdot [{@diff(p2,v)@}] \\ &amp;\displaystyle =&amp;\displaystyle {@factor(diff(p,v))@} \end{array}\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text/>
    </stackversion>
    <questionvariables>
      <text>v:x;
rdm1:3+rand(3);
p1:log(v);
p2:v*p1;
p:p2^rdm1;</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>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <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>
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    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>factor(diff(p,v))</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
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      <syntaxattribute>0</syntaxattribute>
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      <allowwords/>
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      <checkanswertype>1</checkanswertype>
      <mustverify>1</mustverify>
      <showvalidation>1</showvalidation>
      <options/>
    </input>
    <prt>
      <name>Result</name>
      <value>1.0000000</value>
      <autosimplify>1</autosimplify>
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      <feedbackvariables>
        <text>q:p2/p1;</text>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>Diff</answertest>
        <sans>ans1</sans>
        <tans>factor(diff(p,v))</tans>
        <testoptions>v</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-0-T </trueanswernote>
        <truefeedback format="html">
          <text/>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
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        <falsenextnode>1</falsenextnode>
        <falseanswernote>Result-0-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
      <node>
        <name>1</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>ans1</sans>
        <tans>-factor(diff(p,v))</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>0.0000000</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>Result-1-T </trueanswernote>
        <truefeedback format="html">
          <text><![CDATA[<p>You appear to have lost the minus sign as your answer is the negative of what was expected.</p>]]></text>
        </truefeedback>
        <falsescoremode>=</falsescoremode>
        <falsescore>0.0000000</falsescore>
        <falsepenalty/>
        <falsenextnode>-1</falsenextnode>
        <falseanswernote>Result-1-F </falseanswernote>
        <falsefeedback format="html">
          <text/>
        </falsefeedback>
      </node>
    </prt>
    <deployedseed>1494294994</deployedseed>
    <deployedseed>936613491</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ev(factor(diff(p,v)),simp)</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>Result-0-T</expectedanswernote>
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    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>-factor(diff(p,v))</value>
      </testinput>
      <expected>
        <name>Result</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>Result-1-T </expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
