// Numbas version: exam_results_page_options
{"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": [{"functions": {}, "ungrouped_variables": ["c", "p", "np", "d"], "name": "Differentiation 10 - Chain Rule", "tags": [], "advice": "<p>If you don't know how to complete these questions, please see&nbsp;<em>'Differentiation 9 - Chain Rule'</em>.</p>", "rulesets": {}, "parts": [{"variableReplacements": [], "prompt": "<p>$\\simplify{({c[0]}x+{d[0]})^({np[0]})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{np[0]}*{c[0]}*({c[0]}x+{d[0]})^({np[0]}-1)", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p>$\\simplify{({c[1]}x+{d[1]})^(-1)}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "-1*{c[1]}*({c[1]}x+{d[1]})^(-2)", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p>$\\simplify{({c[2]}x^2+{d[2]})^({np[2]})}$</p>", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{np[2]}*2{c[2]}*x*({c[2]}x^2+{d[2]})^({np[2]}-1)", "marks": "2", "checkvariablenames": true, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p>$\\simplify{({c[3]}x^3+{d[3]})^({np[3]})}$</p>", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{np[3]}*3{c[3]}*x^2*({c[3]}x^3+{d[3]})^({np[3]}-1)", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p>$\\simplify{({c[4]}x^2+{d[4]})^({np[4]}/9)}$</p>", "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({np[4]}*2{c[4]}/9)*x*({c[4]}x^2+{d[4]})^(({np[4]}-9)/9)", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p>$\\simplify{sqrt({c[5]}x+{d[5]})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "1/2*{c[5]}*({c[5]}x+{d[5]})^(-1/2)", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "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 the power $0$ in your answer.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"np": {"definition": "repeat(random(-5..-2),10)", "templateType": "anything", "group": "Ungrouped variables", "name": "np", "description": "<p>negative power</p>"}, "p": {"definition": "repeat(random(2..5),10)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": "<p>power</p>"}, "c": {"definition": "repeat(random(2..5),10)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": "<p>coefficient</p>"}, "d": {"definition": "repeat(random(-8..5 except 0),10)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"notes": "", "description": "<p>Using the chain rule with polynomials and negative powers</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}]}