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{"name": "Differentiation - Chain Rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "advice": "<p>\\(f(x)=({\\var{a2}x^{\\var{a3}}+\\var{a4}})^\\var{a1}\\)</p>\n<p>Recall the chain rule: &nbsp; \\(\\frac{df}{dx}=\\frac{df}{du}.\\frac{du}{dx}\\)</p>\n<p style=\"padding-left: 30px;\">let \\(u=\\var{a2}x^{\\var{a3}}+\\var{a4}\\) &nbsp; &nbsp;then &nbsp;&nbsp;\\(f(x)=u^\\var{a1}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{du}=\\var{a1}u^{\\var{a1}-1}\\) &nbsp;and &nbsp;\\(\\frac{du}{dx}=\\var{a3}*\\var{a2}x^{\\var{a3}-1}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=\\var{a1}u^{\\simplify{{a1}-1}}.\\simplify{{a2}*{a3}x^{{a3}-1}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=\\simplify{{a1}*{a2}*{a3}x^{{a3}-1}}({\\var{a2}x^{\\var{a3}}+\\var{a4}})^{\\simplify{{a1}-1}}\\)</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Differentiate the function:</p>\n<p style=\"padding-left: 30px;\">\\(f(x)=({\\var{a2}x^{\\var{a3}}+\\var{a4}})^\\var{a1}\\)</p>", "extensions": [], "preamble": {"css": "", "js": ""}, "tags": [], "parts": [{"gaps": [{"vsetRange": [0, 1], "variableReplacementStrategy": "originalfirst", "failureRate": 1, "unitTests": [], "valuegenerators": [{"name": "x", "value": ""}], "answer": "({a1}*{a2}*{a3}x^{{a3}-1})({a2}x^{{a3}}+{a4})^{{a1}-1}", "customMarkingAlgorithm": "", "scripts": {}, "adaptiveMarkingPenalty": 0, "variableReplacements": [], "showFeedbackIcon": true, "customName": "", "checkingAccuracy": 0.001, "showCorrectAnswer": true, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "marks": "2", "showPreview": true, "vsetRangePoints": 5, "useCustomName": false, "type": "jme", "checkVariableNames": false}], "sortAnswers": false, "customName": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>\\(\\frac{df}{dx}=\\)[[0]]</p>", "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "type": "gapfill", "useCustomName": false, "adaptiveMarkingPenalty": 0, "variableReplacements": [], "showFeedbackIcon": true}], "functions": {}, "name": "Differentiation - Chain Rule", "variables": {"a2": {"name": "a2", "definition": "random(2 .. 6#1)", "description": "", "templateType": "randrange", "group": "Ungrouped variables"}, "a4": {"name": "a4", "definition": "random(1 .. 14#1)", "description": "", "templateType": "randrange", "group": "Ungrouped variables"}, "a1": {"name": "a1", "definition": "random(2 .. 8#1)", "description": "", "templateType": "randrange", "group": "Ungrouped variables"}, "a3": {"name": "a3", "definition": "random(1 .. 4#1)", "description": "", "templateType": "randrange", "group": "Ungrouped variables"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Chain rule</p>"}, "ungrouped_variables": ["a1", "a2", "a3", "a4"], "variable_groups": [], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Kevin Bohan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3363/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Kevin Bohan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3363/"}]}