// Numbas version: exam_results_page_options
{"name": "Sheet 2 Q6 Derivative of exponential with custom feedback", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Sheet 2 Q6 Derivative of exponential with custom feedback", "tags": [], "metadata": {"description": "Differentiation by rule question with feedback given for anticipated student errors.", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Evaluate the derivative of $f(x)=e^{\\cos x + 1}$ at the point $(\\pi,1)$.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "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>First, determine $f'(x)$:</p>\n<p>$f'(x) = $ [[0]]</p>\n<p>Now, evaluate the derivative at the point $(\\pi, 1)$:</p>\n<p>$f'(\\pi)=$ [[1]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"sin(x)*e^(cos(x)+1)\", \"Double check the rule for differentiating $\\\\cos x$.\"],\n    [\"(cos(x)+1)*e^(cos(x))\", \"The power rule is only valid for a variable to the power of a number (e.g. $x^6$). Therefore, you cannot use the power rule for $e^{\\\\cos x + 1}$ (since the variable is in the power).\"],\n    [\"e^(cos(x)+1)\", \"You're on the right track. The exponential function does not change when differentiated. However, when the power is more complicated than a single variable (e.g. $x$) on its own, what extra step do you need to perform?\"],\n    [\"e^(-sin(x))\", \"Remember, the power on the exponential never changes when you differentiate it!\"],\n    [\"e^(-sin(x)+1)\", \"Remember, the power on the exponential never changes when you differentiate it!\"],\n    [\"-sin(x+1)*e^(cos(x+1))\", \"Be very careful when deciding what the argument of cosine is. The +1 is not part of the angle, as there are no brackets to group it with that $x$. The function is $e^{\\\\cos(x)+1}$.\"],\n    [\"sin(x+1)*e^(cos(x+1))\", \"Be very careful when deciding what the argument of cosine is. The +1 is not part of the angle, as there are no brackets to group it with that $x$. The function is $e^{\\\\cos(x)+1}$. Also, double-check the rule for differentiating $\\\\cos x$.\"]\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, "answer": "-sin(x)*e^(cos(x)+1)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "malrules:\n  [\n    [\"-0.404339238\", \"It looks like you have your calculator set to degrees rather than radians. For this module, make sure to always use radians.\"],\n    [\"0.404339238\", \"First, double check the rule for differentiating $\\\\cos x$. Secondly, it looks like you have your calculator set to degrees rather than radians. For this module, make sure to always use radians.\"],\n    [\"1\", \"Check your answer for $f'(x)$. Remember, the power on the exponential never changes when you differentiate it!\"],\n    [\"2.718281828\", \"Check your answer for $f'(x)$. Remember the power on the exponential never changes when you differentiate it!\"],\n    [\"0.946670994\", \"Check your answer for $f'(x)$. Remember the power on the exponential never changes when you differentiate it! Next, make sure your calculator is set to radians rather than degrees.\"],\n    [\"2.573318561\", \"Check your answer for $f'(x)$. Remember the power on the exponential never changes when you differentiate it! Next, make sure your calculator is set to radians rather than degrees.\"],\n    [\"7.377959795\", \"Remember, the exponential function does not change when differentiated. However, when the power is more complicated than a single variable (e.g. $x$) on its own, what extra step do you need to perform? Also, make sure your calculator is set to radians rather than degrees.\"]\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, "answer": "0", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "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/"}]}