// Numbas version: exam_results_page_options
{"name": "Power rule 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "extensions": [], "name": "Power rule 2", "preamble": {"css": "", "js": ""}, "parts": [{"variableReplacements": [], "scripts": {}, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "marks": 0, "prompt": "<p>\\(\\frac{df}{dx}=\\)&nbsp;[[0]]</p>", "type": "gapfill", "gaps": [{"variableReplacements": [], "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "type": "jme", "answer": "-{a1}*{a2}/x^{{a2}+1}+(1/{a3})x^{1/{a3}-1}", "scripts": {}, "checkingaccuracy": 0.001, "vsetrangepoints": 5, "showpreview": true, "checkingtype": "absdiff", "showCorrectAnswer": true, "vsetrange": [0, 1], "marks": 1, "expectedvariablenames": []}]}], "metadata": {"description": "<p>Power rule</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "<p>\\(f(x)=\\frac{\\var{a1}}{x^{\\var{a2}}}+\\sqrt[\\var{a3}]{x}\\)</p>\n<p>\\(f(x)=\\var{a1}x^{-\\var{a2}}+{x}^{\\frac{1}{\\var{a3}}}\\)</p>\n<p>\\(\\frac{df}{dx}=-\\var{a2}*\\var{a1}x^{-\\var{a2}-1}+\\frac{1}{\\var{a3}}{x}^{\\frac{1}{\\var{a3}}-1}\\)</p>\n<p>\\(\\frac{df}{dx}=-\\simplify{{a2}*{a1}x^{-{a2}-1}}+\\frac{1}{\\var{a3}}{x}^{\\simplify{{1-{a3}}/{a3}}}\\)</p>\n<p></p>", "ungrouped_variables": ["a1", "a2", "a3"], "tags": [], "functions": {}, "rulesets": {}, "variables": {"a2": {"group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "a2", "definition": "random(2..8#1)"}, "a3": {"group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "a3", "definition": "random(3..6#1)"}, "a1": {"group": "Ungrouped variables", "templateType": "randrange", "description": "", "name": "a1", "definition": "random(6..18#1)"}}, "statement": "<p>Differentiate the function:</p>\n<p style=\"padding-left: 30px;\">\\(f(x)=\\frac{\\var{a1}}{x^{\\var{a2}}}+\\sqrt[\\var{a3}]{x}\\)</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/"}]}