// Numbas version: finer_feedback_settings
{"name": "Chain rule 4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "variable_groups": [], "tags": [], "parts": [{"variableReplacementStrategy": "originalfirst", "customName": "", "showCorrectAnswer": true, "showFeedbackIcon": true, "sortAnswers": false, "variableReplacements": [], "scripts": {}, "marks": 0, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "useCustomName": false, "gaps": [{"variableReplacementStrategy": "originalfirst", "customName": "", "failureRate": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "vsetRangePoints": 5, "checkingType": "absdiff", "variableReplacements": [], "valuegenerators": [{"name": "x", "value": ""}], "scripts": {}, "marks": "2", "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "vsetRange": [0, 1], "useCustomName": false, "answer": "({a1}*{a2}*{a3}x^{{a3}-1})({a2}x^{{a3}}+{a4})^{{a1}-1}", "unitTests": [], "type": "jme", "showPreview": true, "checkVariableNames": false}], "unitTests": [], "type": "gapfill", "prompt": "<p>\\(\\frac{df}{dx}=\\)[[0]]</p>"}], "functions": {}, "name": "Chain rule 4", "ungrouped_variables": ["a1", "a2", "a3", "a4"], "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Chain rule</p>"}, "extensions": [], "statement": "<p>Differentiate the function:</p>\n<p style=\"padding-left: 30px;\">\\(f(x)=({\\var{a2}x^{\\var{a3}}+\\var{a4}})^\\var{a1}\\)</p>", "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>", "variables": {"a4": {"description": "", "definition": "random(1 .. 14#1)", "group": "Ungrouped variables", "name": "a4", "templateType": "randrange"}, "a2": {"description": "", "definition": "random(2 .. 6#1)", "group": "Ungrouped variables", "name": "a2", "templateType": "randrange"}, "a3": {"description": "", "definition": "random(1 .. 4#1)", "group": "Ungrouped variables", "name": "a3", "templateType": "randrange"}, "a1": {"description": "", "definition": "random(2 .. 8#1)", "group": "Ungrouped variables", "name": "a1", "templateType": "randrange"}}, "type": "question", "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/"}], "resources": []}]}], "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/"}]}