// Numbas version: exam_results_page_options
{"name": "T6Q2 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "metadata": {"description": "<p>Partial differentiation question with customised feedback to catch some common errors.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "parts": [{"scripts": {}, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "unitTests": [], "prompt": "<p>$f_x(x,y)=$ [[0]]</p>", "sortAnswers": false, "showCorrectAnswer": true, "gaps": [{"vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "scripts": {}, "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"(x^2+2*x)*e^x\", \"Be careful when differentiating the exponential function. The power on the exponential function never changes when you differentiate.\"],\n    [\"2x*e^(x+y)\", \"Don't forget to use the product rule to differentiate the first term!\"],  \n    [\"2x*e^(x+y)+x^2*e^(x+y)+sin(y)\", \"Remember, when partially differentiating with respect to $x$ you treat $y$ as a number. Therefore anything to do with $y$ - such as $\\\\cos y$ - is treated as a number.\"],  \n    [\"x^2*e^x+2x*e^(x+y)\", \"Be careful when differentiating the exponential function. The power on the exponential function never changes when you differentiate.\"],\n    [\"x^2*e^(x+y)*(dy)/(dx)+2x*e^(x+y)+sin(y)*(dy)/(dx)\", \"Remember with partial differentiation, $x$ and $y$ are independent of each other. In particular, $y$ does not depend on $x$, so when differentiating with respect to $x$, $y$ is treated like a number.\"],\n    [\"(-x^2*e^(x+y)-2x*e^(x+y))/sin(y)\", \"It looks like you have tried to use implicit differentiation rather than partial differentiation. Implicit differentiation is only used if you wish to find $\\\\frac{dy}{dx}$, not if you wish to find $\\\\frac{\\\\partial y}{\\\\partial x}$ or $f_{x}$ etc.\"],\n    [\"-2x*e^(x+y)/(x^2*e^(x+y)+sin(y))\", \"It looks like you have tried to use implicit differentiation rather than partial differentiation. Implicit differentiation is only used if you wish to find $\\\\frac{dy}{dx}$, not if you wish to find $\\\\frac{\\\\partial y}{\\\\partial x}$ or $f_{x}$ etc.\"]\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) ", "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "answer": "x^2*e^(x+y)+2x*e^(x+y)", "showPreview": true, "expectedVariableNames": [], "failureRate": 1, "marks": 1, "vsetRangePoints": 5, "type": "jme", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}], "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "gapfill", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}, {"scripts": {}, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "unitTests": [], "prompt": "<p>$f_y(x,y)=$ [[0]]</p>", "sortAnswers": false, "showCorrectAnswer": true, "gaps": [{"vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "scripts": {}, "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"x^2*e^(x+y)+2x*e^(x+y)+sin(y)\", \"There is no need for the product rule when differentiating $x^2 e^{x+y}$ since $x$ is treated like a number when partially differentiating with respect to $y$.\"],\n    [\"x^2*e^y+sin(y)\", \"Be careful when differentiating the exponential function. The power on the exponential function never changes when you differentiate.\"],\n    [\"(-x^2*e^(x+y)-2x*e^(x+y))/cos(y)\", \"It looks like you have tried to use implicit differentiation rather than partial differentiation. Implicit differentiation is only used if you wish to find $\\\\frac{dy}{dx}$, not if you wish to find $\\\\frac{\\\\partial y}{\\\\partial x}$ or $\\\\frac{\\\\partial z}{\\\\partial y}$ or $f_{y}$ etc.\"],\n    [\"-2x*e^(x+y)/(x^2*e^(x+y)+cos(y))\", \"It looks like you have tried to use implicit differentiation rather than partial differentiation. Implicit differentiation is only used if you wish to find $\\\\frac{dy}{dx}$, not if you wish to find $\\\\frac{\\\\partial y}{\\\\partial x}$ or $\\\\frac{\\\\partial z}{\\\\partial y}$ or $f_{y}$ etc.\"]\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) ", "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "answer": "x^2*e^(x+y)+sin(y)", "showPreview": true, "expectedVariableNames": [], "failureRate": 1, "marks": 1, "vsetRangePoints": 5, "type": "jme", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}], "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "gapfill", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}, {"scripts": {}, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "unitTests": [], "prompt": "<p>$f_{xy}(x,y)=$ [[0]]</p>", "sortAnswers": false, "showCorrectAnswer": true, "gaps": [{"vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "scripts": {}, "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"x^2*e^(x+y)+4x*e^(x+y)+2e^(x+y)\", \"There is no need for the product rule when differentiating $x^2 e^{x+y}$ since $x$ is treated like a number when partially differentiating with respect to $y$. For the same reason, the product rule is not needed when differentiating $2xe^{x+y}$.\"],\n    [\"x^2*e^y+2x*e^y\", \"Be careful when differentiating the exponential function. The power on the exponential function never changes when you differentiate.\"]\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) ", "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "answer": "x^2*e^(x+y)+2x*e^(x+y)", "showPreview": true, "expectedVariableNames": [], "failureRate": 1, "marks": 1, "vsetRangePoints": 5, "type": "jme", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}], "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "gapfill", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}, {"scripts": {}, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "unitTests": [], "prompt": "<p>$f_{yy}(x,y)=$ [[0]]</p>", "sortAnswers": false, "showCorrectAnswer": true, "gaps": [{"vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "scripts": {}, "checkVariableNames": false, "customMarkingAlgorithm": "malrules:\n  [\n    [\"x^2*e^(x+y)+2x*e^(x+y)+cos(y)\", \"There is no need for the product rule when differentiating $x^2 e^{x+y}$ since $x$ is treated like a number when partially differentiating with respect to $y$.\"],\n    [\"x^2*e^y+cos(y)\", \"Be careful when differentiating the exponential function. The power on the exponential function never changes when you differentiate.\"]\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) ", "unitTests": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "checkingAccuracy": 0.001, "checkingType": "absdiff", "answer": "x^2*e^(x+y)+cos(y)", "showPreview": true, "expectedVariableNames": [], "failureRate": 1, "marks": 1, "vsetRangePoints": 5, "type": "jme", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}], "extendBaseMarkingAlgorithm": true, "marks": 0, "type": "gapfill", "variableReplacements": [], "variableReplacementStrategy": "originalfirst"}], "functions": {}, "statement": "<p>If $f(x,y)=x^2e^{x+y}-\\cos y$, find the partial derivatives:</p>", "preamble": {"css": "", "js": ""}, "name": "T6Q2 (custom feedback)", "extensions": [], "rulesets": {}, "ungrouped_variables": [], "advice": "", "variables": {}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "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/"}]}