// Numbas version: finer_feedback_settings
{"name": "Power rule 1b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "statement": "<ul>\n<li>Differentiate the following:</li>\n</ul>\n<p style=\"padding-left: 30px;\">\\(y=\\var{a}x^{\\var{b}}+\\var{c}x^{\\var{d}}+\\var{f}\\)</p>", "variable_groups": [], "ungrouped_variables": ["a", "b", "c", "d", "f"], "variables": {"f": {"group": "Ungrouped variables", "description": "", "definition": "random(3 .. 18#1)", "name": "f", "templateType": "randrange"}, "a": {"group": "Ungrouped variables", "description": "", "definition": "random(2 .. 10#1)", "name": "a", "templateType": "randrange"}, "b": {"group": "Ungrouped variables", "description": "", "definition": "random(-12 .. -3#1)", "name": "b", "templateType": "randrange"}, "c": {"group": "Ungrouped variables", "description": "", "definition": "random(2 .. 14#1)", "name": "c", "templateType": "randrange"}, "d": {"group": "Ungrouped variables", "description": "", "definition": "random(1 .. 5#0.25)", "name": "d", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Power rule</p>"}, "parts": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "customName": "", "prompt": "<p>\\(\\frac{dy}{dx}=\\)&nbsp;[[0]]</p>", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 1, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "customName": "", "answer": "{a}*{b}*x^{{b}-1}+{c}*{d}*x^{{d}-1}", "showCorrectAnswer": true, "checkingAccuracy": 0.001, "checkVariableNames": false, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "type": "jme", "vsetRange": [0, 1], "useCustomName": false, "showFeedbackIcon": true, "showPreview": true, "valuegenerators": [{"value": "", "name": "x"}], "variableReplacements": [], "scripts": {}}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}}], "advice": "<p>Apply&nbsp;the rule:</p>\n<p style=\"padding-left: 30px;\">\\(y=ax^n\\,\\,\\,then\\,\\,\\,\\frac{dy}{dx}=nax^{n-1}\\)</p>\n<p>In this example</p>\n<p style=\"padding-left: 30px;\">\\(y=\\var{a}x^{\\var{b}}+\\var{c}x^{\\var{d}}+\\var{f}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{dy}{dx}=\\var{b}*\\var{a}x^{\\var{b}-1}+\\var{d}*\\var{c}x^{\\var{d}-1}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{dy}{dx}=\\simplify{{b}*{a}x^{{b}-1}+{d}*{c}x^{{d}-1}}\\)</p>", "functions": {}, "rulesets": {}, "extensions": [], "name": "Power rule 1b", "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/"}, {"name": "Kamila Yusufu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2554/"}]}]}], "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": "Kamila Yusufu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2554/"}]}