// Numbas version: exam_results_page_options {"name": "Jinhua's copy of 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": {}, "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "

Using the chain rule with polynomials and negative powers

"}, "statement": "

Differentiate the following polynomials with respect to $x$.

\n

Give your answer in the form $ax^{b}(cx^d+e)^f$, where $f$ is a negative power.

\n

It is not necessary to include powers of $1$ or terms to the power $0$ in your answer.

", "preamble": {"css": "", "js": ""}, "advice": "

If you don't know how to complete these questions, please see 'Differentiation 9 - Chain Rule'.

", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "answersimplification": "all", "answer": "{np[0]}*{c[0]}*({c[0]}x+{d[0]})^({np[0]}-1)", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "vsetrange": [0, 1], "checkingtype": "absdiff", "marks": "2", "showpreview": true, "prompt": "

$\\simplify{({c[0]}x+{d[0]})^({np[0]})}$

", "scripts": {}}, {"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "answersimplification": "all", "answer": "-1*{c[1]}*({c[1]}x+{d[1]})^(-2)", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "vsetrange": [0, 1], "checkingtype": "absdiff", "marks": "2", "showpreview": true, "prompt": "

$\\simplify{({c[1]}x+{d[1]})^(-1)}$

", "scripts": {}}, {"expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "answersimplification": "all", "answer": "{np[2]}*2{c[2]}*x*({c[2]}x^2+{d[2]})^({np[2]}-1)", "checkvariablenames": true, "variableReplacementStrategy": "originalfirst", "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "vsetrange": [0, 1], "checkingtype": "absdiff", "marks": "2", "showpreview": true, "prompt": "

$\\simplify{({c[2]}x^2+{d[2]})^({np[2]})}$

", "scripts": {}}, {"expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "answersimplification": "all", "answer": "{np[3]}*3{c[3]}*x^2*({c[3]}x^3+{d[3]})^({np[3]}-1)", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "vsetrange": [0, 1], "checkingtype": "absdiff", "marks": "2", "showpreview": true, "prompt": "

$\\simplify{({c[3]}x^3+{d[3]})^({np[3]})}$

", "scripts": {}}, {"expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "answersimplification": "all", "answer": "({np[4]}*2{c[4]}/9)*x*({c[4]}x^2+{d[4]})^(({np[4]}-9)/9)", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "vsetrange": [0, 1], "checkingtype": "absdiff", "marks": "2", "showpreview": true, "prompt": "

$\\simplify{({c[4]}x^2+{d[4]})^({np[4]}/9)}$

", "scripts": {}}, {"expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrangepoints": 5, "answersimplification": "all", "answer": "1/2*{c[5]}*({c[5]}x+{d[5]})^(-1/2)", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "type": "jme", "showCorrectAnswer": true, "variableReplacements": [], "vsetrange": [0, 1], "checkingtype": "absdiff", "marks": "2", "showpreview": true, "prompt": "

$\\simplify{sqrt({c[5]}x+{d[5]})}$

", "scripts": {}}], "type": "question", "variable_groups": [], "rulesets": {}, "name": "Jinhua's copy of Differentiation 10 - Chain Rule", "variables": {"p": {"templateType": "anything", "name": "p", "definition": "repeat(random(2..5),10)", "description": "

power

", "group": "Ungrouped variables"}, "np": {"templateType": "anything", "name": "np", "definition": "repeat(random(-5..-2),10)", "description": "

negative power

", "group": "Ungrouped variables"}, "d": {"templateType": "anything", "name": "d", "definition": "repeat(random(-8..5 except 0),10)", "description": "", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "name": "c", "definition": "repeat(random(2..5),10)", "description": "

coefficient

", "group": "Ungrouped variables"}}, "question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0, "name": ""}], "tags": [], "showQuestionGroupNames": false, "ungrouped_variables": ["c", "p", "np", "d"], "contributors": [{"name": "Jean jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}]}], "contributors": [{"name": "Jean jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}