// Numbas version: exam_results_page_options {"name": "MathJax v3", "timing": {"timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}, "allowPause": true}, "metadata": {"description": "This exam uses a theme which uses MathJax v3 to typeset mathematics.
", "licence": "Creative Commons Attribution 4.0 International"}, "duration": 0, "showstudentname": true, "showQuestionGroupNames": false, "navigation": {"reverse": true, "browse": true, "showresultspage": "oncompletion", "allowsteps": true, "preventleave": true, "allowregen": true, "onleave": {"action": "none", "message": ""}, "startpassword": "", "showfrontpage": true}, "feedback": {"allowrevealanswer": true, "showtotalmark": true, "showactualmark": true, "intro": "", "feedbackmessages": [], "advicethreshold": 0, "showanswerstate": true}, "percentPass": 0, "question_groups": [{"name": "Group", "pickQuestions": 1, "pickingStrategy": "all-ordered", "questions": [{"name": "Numbas demo: JME part", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}], "variables": {"num_terms": {"name": "num_terms", "description": "", "templateType": "anything", "definition": "3", "group": "Ungrouped variables"}, "powers": {"name": "powers", "description": "", "templateType": "anything", "definition": "sort(shuffle(list(0..8))[0..3])", "group": "Ungrouped variables"}, "coefficients": {"name": "coefficients", "description": "", "templateType": "anything", "definition": "repeat(random(-10..10 except 0),num_terms)", "group": "Ungrouped variables"}}, "parts": [{"unitTests": [], "marks": 0, "sortAnswers": false, "steps": [{"unitTests": [], "marks": 0, "variableReplacements": [], "showCorrectAnswer": true, "prompt": "

The derivative of $x^n$ is given by the following:

\n

\$\\frac{\\mathrm{d}}{\\mathrm{d}x}(x^n) = n \\times x^{n-1} \$

\n

Enter the derivatives of each of the three terms in $f(x)$:

", "customMarkingAlgorithm": "", "type": "information", "scripts": {}, "customName": "", "useCustomName": false, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}, {"valuegenerators": [{"name": "x", "value": ""}], "vsetRange": [0, 1], "unitTests": [], "checkingAccuracy": 0.001, "marks": 1, "vsetRangePoints": 5, "answer": "{coefficients[2]*powers[2]}*x^{powers[2]-1}", "variableReplacements": [], "type": "jme", "customName": "", "useCustomName": false, "checkVariableNames": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

$\\frac{\\mathrm{d}}{\\mathrm{d}x}(\\simplify{{coefficients[2]}*x^{powers[2]}}) =$

", "failureRate": 1, "checkingType": "absdiff", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showPreview": true, "variableReplacementStrategy": "originalfirst"}, {"valuegenerators": [{"name": "x", "value": ""}], "vsetRange": [0, 1], "unitTests": [], "checkingAccuracy": 0.001, "marks": 1, "vsetRangePoints": 5, "answer": "{coefficients[1]*powers[1]}*x^{powers[1]-1}", "variableReplacements": [], "type": "jme", "customName": "", "useCustomName": false, "checkVariableNames": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

$\\frac{\\mathrm{d}}{\\mathrm{d}x}(\\simplify{{coefficients[1]}*x^{powers[1]}}) =$

", "failureRate": 1, "checkingType": "absdiff", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showPreview": true, "variableReplacementStrategy": "originalfirst"}, {"valuegenerators": [{"name": "x", "value": ""}], "vsetRange": [0, 1], "unitTests": [], "checkingAccuracy": 0.001, "marks": 1, "vsetRangePoints": 5, "answer": "{coefficients[0]*powers[0]}*x^{powers[0]-1}", "variableReplacements": [], "type": "jme", "customName": "", "useCustomName": false, "checkVariableNames": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

$\\frac{\\mathrm{d}}{\\mathrm{d}x}(\\simplify{{coefficients[0]}*x^{powers[0]}}) =$

", "failureRate": 1, "checkingType": "absdiff", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showPreview": true, "variableReplacementStrategy": "originalfirst"}], "variableReplacements": [], "showCorrectAnswer": true, "prompt": "

Differentiate the following function.

\n

\$f(x) = \\simplify[all,!noLeadingMinus]{ {coefficients[2]}*x^{powers[2]} + {coefficients[1]}*x^{powers[1]} + {coefficients[0]}*x^{powers[0]} } \$

\n

$\\frac{\\mathrm{d}f}{\\mathrm{d}x} =$ [[0]]

", "stepsPenalty": "1", "gaps": [{"valuegenerators": [{"name": "x", "value": ""}], "vsetRange": [0, 1], "unitTests": [], "checkingAccuracy": 0.001, "marks": "4", "vsetRangePoints": 5, "answer": "{coefficients[2]*powers[2]}*x^{powers[2]-1} + {coefficients[1]*powers[1]}*x^{powers[1]-1} + {coefficients[0]*powers[0]}*x^{powers[0]-1}", "showFeedbackIcon": true, "variableReplacements": [], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "checkingType": "absdiff", "type": "jme", "scripts": {}, "customName": "", "useCustomName": false, "failureRate": 1, "checkVariableNames": false, "showPreview": true, "variableReplacementStrategy": "originalfirst"}], "customMarkingAlgorithm": "", "type": "gapfill", "scripts": {}, "customName": "", "useCustomName": false, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "variable_groups": [], "tags": [], "ungrouped_variables": ["num_terms", "powers", "coefficients"], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Numbas is really good at creating and marking randomised maths questions. In this question, you're given a random polynomial to differentiate.

\n

Notice how Numbas automatically simplifies the mathematical expressions so they look as if a human wrote them.

\n

See this question in the public editor

The derivative of $x^n$ is given by the following:

\n

\$\\frac{\\mathrm{d}}{\\mathrm{d}x}(x^n) = n \\times x^{n-1} \$

\n

We can compute the derivative of $f(x)$ by computing the derivatives of each of the three terms, and then adding them together.

\n

\\begin{align}
\\frac{\\mathrm{d}}{\\mathrm{d}x}(\\simplify{{coefficients[2]}*x^{powers[2]}}) &= \\simplify[basic]{{powers[2]}*{coefficients[2]}*x^({powers[2]}-1)} \\\\
&= \\simplify{{coefficients[2]*powers[2]}*x^{powers[2]-1}}
\\end{align}

\n

\\begin{align}
\\frac{\\mathrm{d}}{\\mathrm{d}x}(\\simplify{{coefficients[1]}*x^{powers[1]}}) &= \\simplify[basic]{{powers[1]}*{coefficients[1]}*x^({powers[1]}-1)} \\\\
&= \\simplify{{coefficients[1]*powers[1]}*x^{powers[1]-1}}
\\end{align}

\n

The derivative of a constant is $0$. So,

\n

\$\\frac{\\mathrm{d}}{\\mathrm{d}x}(\\var{coefficients[0]}) = 0 \$

\n

\\begin{align}
\\frac{\\mathrm{d}}{\\mathrm{d}x}(\\simplify{{coefficients[0]}*x^{powers[0]}}) &= \\simplify[basic]{{powers[0]}*{coefficients[0]}*x^({powers[0]}-1)} \\\\
&= \\simplify{{coefficients[0]*powers[0]}*x^{powers[0]-1}}
\\end{align}

\n

Hence,

\n

\$\\frac{\\mathrm{d}f}{\\mathrm{d}x} = \\simplify{ {coefficients[2]*powers[2]}*x^{powers[2]-1} + {coefficients[1]*powers[1]}*x^{powers[1]-1} + {coefficients[0]*powers[0]}*x^{powers[0]-1} } \$

", "functions": {}, "rulesets": {}}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "extensions": [], "custom_part_types": [], "resources": []}