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{"name": "Differentiation 10 - Chain Rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "ungrouped_variables": ["c", "p", "np", "d"], "advice": "<p>If you don't know how to complete these questions, please see&nbsp;<em>'Differentiation 9 - Chain Rule'</em>.</p>", "metadata": {"description": "<p>Using the chain rule with polynomials and negative powers</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"prompt": "<p>$\\simplify{({c[0]}x+{d[0]})^({np[0]})}$</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": "2", "checkVariableNames": false, "valuegenerators": [{"value": "", "name": "x"}], "customName": "", "answer": "{np[0]}*{c[0]}*({c[0]}x+{d[0]})^({np[0]}-1)", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all"}, {"prompt": "<p>$\\simplify{({c[1]}x+{d[1]})^(-1)}$</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": "2", "checkVariableNames": false, "valuegenerators": [{"value": "", "name": "x"}], "customName": "", "answer": "-1*{c[1]}*({c[1]}x+{d[1]})^(-2)", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all"}, {"prompt": "<p>$\\simplify{({c[2]}x^2+{d[2]})^({np[2]})}$</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": "2", "checkVariableNames": true, "valuegenerators": [{"value": "", "name": "x"}], "customName": "", "answer": "{np[2]}*2{c[2]}*x*({c[2]}x^2+{d[2]})^({np[2]}-1)", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all"}, {"prompt": "<p>$\\simplify{({c[3]}x^3+{d[3]})^({np[3]})}$</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": "2", "checkVariableNames": false, "valuegenerators": [{"value": "", "name": "x"}], "customName": "", "answer": "{np[3]}*3{c[3]}*x^2*({c[3]}x^3+{d[3]})^({np[3]}-1)", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all"}, {"prompt": "<p>$\\simplify{({c[4]}x^2+{d[4]})^({np[4]}/9)}$</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": "2", "checkVariableNames": false, "valuegenerators": [{"value": "", "name": "x"}], "customName": "", "answer": "({np[4]}*2{c[4]}/9)*x*({c[4]}x^2+{d[4]})^(({np[4]}-9)/9)", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all"}, {"prompt": "<p>$\\simplify{sqrt({c[5]}x+{d[5]})}$</p>", "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "customMarkingAlgorithm": "", "type": "jme", "showFeedbackIcon": true, "useCustomName": false, "checkingAccuracy": 0.001, "vsetRangePoints": 5, "showCorrectAnswer": true, "marks": "2", "checkVariableNames": false, "valuegenerators": [{"value": "", "name": "x"}], "customName": "", "answer": "1/2*{c[5]}*({c[5]}x+{d[5]})^(-1/2)", "showPreview": true, "scripts": {}, "variableReplacements": [], "unitTests": [], "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "failureRate": 1, "answerSimplification": "all"}], "tags": [], "statement": "<p><strong>Differentiate the following polynomials with respect to $x$.</strong></p>\n<p>Give&nbsp;your answer in the form $ax^{b}(cx^d+e)^f$, where $f$ is a negative power.</p>\n<p>It is not necessary to include powers of $1$ or terms to 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