// Numbas version: finer_feedback_settings
{"name": "Power rule 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Power rule</p>"}, "rulesets": {}, "functions": {}, "ungrouped_variables": ["a1", "a2", "b1", "b2", "c1"], "name": "Power rule 1", "statement": "<p>Differentiate the function:</p>\n<p style=\"padding-left: 30px;\">\\(f(x)=\\var{a1}x^{\\var{a2}}+\\var{b1}x^{\\var{b2}}+\\var{c1}\\)</p>", "preamble": {"css": "", "js": ""}, "variables": {"a1": {"definition": "random(2..10#1)", "description": "", "templateType": "randrange", "name": "a1", "group": "Ungrouped variables"}, "b1": {"definition": "random(2..14#1)", "description": "", "templateType": "randrange", "name": "b1", "group": "Ungrouped variables"}, "c1": {"definition": "random(3..18#1)", "description": "", "templateType": "randrange", "name": "c1", "group": "Ungrouped variables"}, "b2": {"definition": "random(1..5#1)", "description": "", "templateType": "randrange", "name": "b2", "group": "Ungrouped variables"}, "a2": {"definition": "random(5..12#1)", "description": "", "templateType": "randrange", "name": "a2", "group": "Ungrouped variables"}}, "variable_groups": [], "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"type": "gapfill", "gaps": [{"answer": "{a1}*{a2}*x^{{a2}-1}+{b1}*{b2}*x^{{b2}-1}", "showpreview": true, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "checkingaccuracy": 0.001, "type": "jme", "marks": 1, "vsetrange": [0, 1], "variableReplacements": [], "vsetrangepoints": 5, "checkingtype": "absdiff", "showCorrectAnswer": true, "scripts": {}, "expectedvariablenames": []}], "prompt": "<p>\\(\\frac{df}{dx}=\\)&nbsp;[[0]]</p>", "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}], "extensions": [], "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;\">\\(f(x)=\\var{a1}x^{\\var{a2}}+\\var{b1}x^{\\var{b2}}+\\var{c1}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=\\var{a2}*\\var{a1}x^{\\var{a2}-1}+\\var{b2}*\\var{b1}x^{\\var{b2}-1}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{dy}{dx}=\\simplify{{a2}*{a1}x^{{a2}-1}+{b2}*{b1}x^{{b2}-1}}\\)</p>", "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}