// Numbas version: exam_results_page_options
{"name": "Differentiation 12 - Product Rule (with Chain Rule)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Using the chain rule within product rule problems</p>"}, "statement": "<p><strong>Differentiate the following expressions with respect to $x$ using the product rule.</strong></p>\n<p><strong></strong>Simplify your answers as much as possible.</p>", "functions": {}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"c": {"templateType": "anything", "name": "c", "description": "", "group": "Ungrouped variables", "definition": "repeat(random(-9..9 except 0),13)"}, "p": {"templateType": "anything", "name": "p", "description": "", "group": "Ungrouped variables", "definition": "repeat(random(2..6),10)"}}, "ungrouped_variables": ["c", "p"], "tags": [], "preamble": {"js": "", "css": ""}, "variable_groups": [], "advice": "<p>If you have trouble with this question, please refer back to&nbsp;<em>'Differentiation 11 - Product Rule (Basic)'</em>&nbsp;and/or&nbsp;<em>'Differentiation 9 - Chain Rule'</em> and make sure you understand fully everything presented to you in the advice section.</p>\n<p>You should then be able to see how to apply the rules to the above questions.</p>", "name": "Differentiation 12 - Product Rule (with Chain Rule)", "parts": [{"showCorrectAnswer": true, "marks": "2", "variableReplacements": [], "valuegenerators": [{"value": "", "name": "x"}], "answerSimplification": "all", "useCustomName": false, "scripts": {}, "customName": "", "type": "jme", "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "vsetRange": [0, 1], "showPreview": true, "checkingAccuracy": 0.001, "prompt": "<p>$\\simplify{x^2(x+{c[0]})^{p[0]}}$</p>", "failureRate": 1, "answer": "2x*(x+{c[0]})^{p[0]}+{p[0]}x^2*(x+{c[0]})^({p[0]}-1)", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": []}, {"showCorrectAnswer": true, "marks": "2", "variableReplacements": [], "valuegenerators": [{"value": "", "name": "x"}], "answerSimplification": "all", "useCustomName": false, "scripts": {}, "customName": "", "type": "jme", "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "vsetRange": [0, 1], "showPreview": true, "checkingAccuracy": 0.001, "prompt": "<p>$\\simplify{{c[1]}x^3({c[2]}x+{c[3]})^{p[1]}}$</p>", "failureRate": 1, "answer": "3{c[1]}x^2*({c[2]}x+{c[3]})^{p[1]}+{p[1]}{c[2]}{c[1]}x^3*({c[2]}x+{c[3]})^({p[1]}-1)", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": []}, {"showCorrectAnswer": true, "marks": "2", "variableReplacements": [], "valuegenerators": [{"value": "", "name": "x"}], "answerSimplification": "all", "useCustomName": false, "scripts": {}, "customName": "", "type": "jme", "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "vsetRange": [0, 1], "showPreview": true, "checkingAccuracy": 0.001, "prompt": "<p>$\\simplify{{c[4]}x^{p[2]}({c[5]}x^2+{c[6]})^{p[3]}}$</p>", "failureRate": 1, "answer": "{p[2]}{c[4]}x^({p[2]}-1)*({c[5]}x^2+{c[6]})^{p[3]}+2{p[3]}{c[4]}{c[5]}x^({p[2]}+1)*({c[5]}x^2+{c[6]})^({p[3]}-1)", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": []}, {"showCorrectAnswer": true, "marks": "2", "variableReplacements": [], "valuegenerators": [{"value": "", "name": "x"}], "answerSimplification": "all", "useCustomName": false, "scripts": {}, "customName": "", "type": "jme", "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "vsetRange": [0, 1], "showPreview": true, "checkingAccuracy": 0.001, "prompt": "<p>$\\simplify{(x+{c[7]})^{p[4]}(x+{c[8]})^{p[5]}}$</p>", "failureRate": 1, "answer": "{p[4]}(x+{c[7]})^({p[4]}-1)*(x+{c[8]})^{p[5]}+{p[5]}(x+{c[8]})^({p[5]}-1)*(x+{c[7]})^{p[4]}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": []}, {"showCorrectAnswer": true, "marks": "2", "variableReplacements": [], "valuegenerators": [{"value": "", "name": "x"}], "answerSimplification": "all", "useCustomName": false, "scripts": {}, "customName": "", "type": "jme", "checkingType": "absdiff", "variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "checkVariableNames": false, "showFeedbackIcon": true, "vsetRange": [0, 1], "showPreview": true, "checkingAccuracy": 0.001, "prompt": "<p>$\\simplify{({c[9]}x^2+{c[10]})^{p[6]}({c[11]}x^2+{c[12]})^{p[7]}}$</p>", "failureRate": 1, "answer": "2{p[6]}{c[9]}x*({c[9]}x^2+{c[10]})^({p[6]}-1)*({c[11]}x^2+{c[12]})^{p[7]}+2{p[7]}{c[11]}x*({c[11]}x^2+{c[12]})^({p[7]}-1)*({c[9]}x^2+{c[10]})^{p[6]}", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "unitTests": []}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}