// Numbas version: exam_results_page_options
{"name": "T6Q7 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "T6Q7 (custom feedback)", "tags": [], "metadata": {"description": "<p>Logarithmic&nbsp;differentiation question with customised feedback to catch some common errors.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>If $y=x^{\\sqrt{x}}$, find $\\displaystyle \\frac{dy}{dx}$.</p>", "advice": "", "rulesets": {}, "extensions": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle \\frac{dy}{dx}=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"sqrt(x)*x^(sqrt(x)-1)\", \"You cannot use the power rule when you have a variable in the power. What method of differentiation do you need when you have variables to the power of variables?\"],\n    [\"1/sqrt(x)+ln(x)/(2*sqrt(x))\", \"Did you forget to multiply both sides by $y$? Remember, when you take the natural log of both sides and then differentiate both sides, the derivative of the left hand side is $\\\\frac{d}{dx} \\\\left( \\\\ln y \\\\right) = \\\\frac{1}{y} \\\\frac{dy}{dx}$, not just $\\\\frac{dy}{dx}$.\"],\n    [\"y*(1/(2x*sqrt(x)))\", \"Take a closer look at what you were trying to differentiate on the right hand side - you should have $\\\\sqrt{x} \\\\ln x$ i.e. one function of $x$ multiplied by another function of $x$. You therefore need the product rule for this.\"],\n    [\"x^(sqrt(x))*(1/(2x*sqrt(x)))\", \"Take a closer look at what you were trying to differentiate on the right hand side - you should have $\\\\sqrt{x} \\\\ln x$ i.e. one function of $x$ multiplied by another function of $x$. You therefore need the product rule for this.\"]\n    ]\n\n\nparsed_malrules: \n    map(\n        [\"expr\":parse(x[0]),\"feedback\":x[1]],\n        x,\n        malrules\n    )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n    map(\n        len(filter(not x ,x,map(\n            try(\n                resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n                message,\n                false\n            ),\n            vars,\n            vset\n        )))<settings[\"failureRate\"],\n        malrule,\n        parsed_malrules\n    )\n\nmatched_malrules:\n  filter(x[0],x,zip(agree_malrules,parsed_malrules))\n  \nmalrule_feedback:\n    assert(numericallyCorrect,\n        assert(len(matched_malrules)=0,\n            set_credit(0,matched_malrules[0][1][\"feedback\"])\n        )\n    )\n\nmark:\n    apply(studentExpr);\n    apply(unexpectedVariables);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty) ", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"sqrt(x)*x^(sqrt(x)-1)\", \"You cannot use the power rule when you have a variable in the power. What method of differentiation do you need when you have variables to the power of variables?\"],\n    [\"1/sqrt(x)+ln(x)/(2*sqrt(x))\", \"Did you forget to multiply both sides by $y$? Remember, when you take the natural log of both sides and then differentiate both sides, the derivative of the left hand side is $\\\\frac{d}{dx} \\\\left( \\\\ln y \\\\right) = \\\\frac{1}{y} \\\\frac{dy}{dx}$, not just $\\\\frac{dy}{dx}$.\"],\n    [\"y*(1/(2x*sqrt(x)))\", \"Take a closer look at what you were trying to differentiate on the right hand side - you should have $\\\\sqrt{x} \\\\ln x$ i.e. one function of $x$ multiplied by another function of $x$. You therefore need the product rule for this.\"],\n    [\"x^(sqrt(x))*(1/(2x*sqrt(x)))\", \"Take a closer look at what you were trying to differentiate on the right hand side - you should have $\\\\sqrt{x} \\\\ln x$ i.e. one function of $x$ multiplied by another function of $x$. You therefore need the product rule for this.\"]\n    ]\n\n\nparsed_malrules: \n    map(\n        [\"expr\":parse(x[0]),\"feedback\":x[1]],\n        x,\n        malrules\n    )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n    map(\n        len(filter(not x ,x,map(\n            try(\n                resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n                message,\n                false\n            ),\n            vars,\n            vset\n        )))<settings[\"failureRate\"],\n        malrule,\n        parsed_malrules\n    )\n\nmatched_malrules:\n  filter(x[0],x,zip(agree_malrules,parsed_malrules))\n  \nmalrule_feedback:\n    assert(numericallyCorrect,\n        assert(len(matched_malrules)=0,\n            set_credit(0,matched_malrules[0][1][\"feedback\"])\n        )\n    )\n\nmark:\n    apply(studentExpr);\n    apply(unexpectedVariables);\n    apply(numericallyCorrect);\n    apply(malrule_feedback);\n    apply(failMinLength);\n    apply(failMaxLength);\n    apply(forbiddenStringsPenalty);\n    apply(requiredStringsPenalty) ", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": false, "answer": "y*(1/sqrt(x)+1/(2sqrt(x))*ln(x))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}]}], "answer": "x^(sqrt(x))*(1/sqrt(x)+1/(2sqrt(x))*ln(x))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}