// Numbas version: finer_feedback_settings
{"name": "Differentiation: standard derivatives, multiple terms, complicated coefficients, randomised", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Differentiation: standard derivatives, multiple terms, complicated coefficients, randomised", "tags": [], "metadata": {"description": "<p>Standard derivatives asked for (e.g. $x^n$, $1/x^n$, $\\sqrt(x)$, $\\ln(x)$, $\\sin(x)$, etc.) .&nbsp;&nbsp;</p>", "licence": "None specified"}, "statement": "", "advice": "<p>See 10.1, 10.2, 10.4 and 10.5.</p>", "rulesets": {}, "extensions": [], "variables": {"f": {"name": "f", "group": "functions", "definition": "[\n  [\"(1*\",\")\"],\n  [\"(\",\")^\"+n1],\n  [\"(\",\")^\"+n2],\n  [\"1/(\",\")\"],\n  [\"1/((\",\")^\"+n3+\")\"],\n  [\"sqrt(\",\")\"],\n  [\"sin(\",\")\"],\n  [\"cos(\",\")\"],\n  [\"e^(\",\")\"],\n  [\"ln(\",\")\"]\n ]", "description": "", "templateType": "anything"}, "f0": {"name": "f0", "group": "functions", "definition": "map(expression(a[j]+\"*\"+f[rand[j]][0]+var+ f[rand[j]][1]),j,0..8)", "description": "", "templateType": "anything"}, "n3": {"name": "n3", "group": "coeffs etc", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "coeffs etc", "definition": "shuffle(map(random(-2..-9),j,0..8)+[0.25,0.2,0.75,0.8,0.1,0.6,2/3])", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "group": "coeffs etc", "definition": "random(2..3)", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "group": "coeffs etc", "definition": "random(7..9)", "description": "", "templateType": "anything"}, "f'": {"name": "f'", "group": "functions", "definition": "[\n  [\"(1*(\",\"^0))\"],\n  [n1+\"*(\",\")^\"+(n1-1)],\n  [n2+\"*(\",\")^\"+(n2-1)],\n  [\"-1/((\",\")^2)\"],\n  [\"-\"+n3+\"/((\",\")^\"+(n3+1)+\")\"],\n  [\"0.5/(sqrt(\",\"))\"],\n  [\"cos(\",\")\"],\n  [\"-sin(\",\")\"],\n  [\"e^(\",\")\"],\n  [\"1/(\",\")\"]\n ]", "description": "", "templateType": "anything"}, "rand": {"name": "rand", "group": "Ungrouped variables", "definition": "shuffle(0..9)", "description": "<p>[<br />0[\"(\"+b0[0]+\"*\",\")\"],<br />1[\"(\",\")^\"+n1],<br />2[\"(\",\")^\"+n2],<br />3[\"1/(\",\")\"],<br />4[\"1/((\",\")^\"+n3+\")\"],<br />5[\"sqrt(\",\")\"],<br />6[\"sin(\",\")\"],<br />7[\"cos(\",\")\"],<br />8[\"e^(\",\")\"],<br />9[\"ln(\",\")\"]<br /> ]</p>\n<p></p>\n<p>don't use 0 for product rule</p>", "templateType": "anything"}, "var": {"name": "var", "group": "coeffs etc", "definition": "random(['x','z','t','p','s','r','w'])", "description": "", "templateType": "anything"}, "f0'": {"name": "f0'", "group": "functions", "definition": "map(expression(a[j]+\"*\"+f'[rand[j]][0]+var+ f'[rand[j]][1]),j,0..8)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["rand"], "variable_groups": [{"name": "coeffs etc", "variables": ["var", "n1", "n2", "n3", "a"]}, {"name": "functions", "variables": ["f", "f'", "f0", "f0'"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>Differentiate the following with respect to $\\simplify{{expression(var)}}$.</p>\n<p></p>\n<p>$\\simplify[fractionNumbers, all]{{f0[0]}+{f0[1]}}$. [[0]]</p>\n<p>$\\simplify[fractionNumbers, all]{{f0[2]}+{f0[3]}+{f0[4]}}$. [[1]]</p>\n<p>$\\simplify[fractionNumbers, all]{{f0[5]}+{f0[6]}+{f0[7]}+{f0[8]}}$. [[2]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0'[0]}+{f0'[1]}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0'[2]}+{f0'[3]}+{f0'[4]}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{f0'[5]}+{f0'[6]}+{f0'[7]}+{f0'[8]}", "answerSimplification": "fractionNumbers, all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "valuegenerators": []}], "sortAnswers": false}], "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}], "resources": []}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}