// Numbas version: exam_results_page_options
{"name": "Product rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a1", "a2", "a3", "a4", "a5"], "name": "Product rule", "tags": [], "advice": "<p>\\(f(x)=(\\var{a1}x^\\var{a2}+\\var{a3})e^{\\var{a4}x+\\var{a5}}\\)</p>\n<p>Recall the product rule if \\(f(x)=u.v\\) where \\(u\\) and \\(v\\) are both functions of \\(x\\) then</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=v.\\frac{du}{dx}+u.\\frac{dv}{dx}\\)</p>\n<p style=\"padding-left: 30px;\">let \\(u=\\var{a1}x^\\var{a2}+\\var{a3}\\) &nbsp;and &nbsp;\\(v=e^{\\var{a4}x+\\var{a5}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{du}{dx}=\\var{a2}*\\var{a1}x^{\\var{a2}-1}\\) &nbsp;and &nbsp;\\(\\frac{dv}{dx}=\\var{a4}*e^{\\var{a4}x+\\var{a5}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=e^{\\var{a4}x+\\var{a5}}*\\var{a2}*\\var{a1}x^{\\var{a2}-1}+(\\var{a1}x^\\var{a2}+\\var{a3})*\\var{a4}*e^{\\var{a4}x+\\var{a5}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=\\simplify{e^({a4}x+{a5})*{a1}*{a2}x^{{a2}-1}+({a1}x^{a2}+{a3})*{a4}*e^({a4}x+{a5})}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=(\\simplify{{a1}*{a4}x^{a2}+{a1}*{a2}x^{{a2}-1}+{a3}*{a4}})\\simplify{e^({a4}x+{a5})}\\)</p>", "rulesets": {}, "parts": [{"prompt": "<p>\\(\\frac{df}{dx}=\\)[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({a1}*{a4}x^{a2}+{a1}*{a2}x^{{a2}-1}+{a3}*{a4})*e^({a4}x+{a5})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Differentiate the function</p>\n<p style=\"padding-left: 30px;\">\\(f(x)=(\\var{a1}x^\\var{a2}+\\var{a3})e^{\\var{a4}x+\\var{a5}}\\)</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a1": {"definition": "random(2..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "random(1..12#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2..5#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(4..15#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a4": {"definition": "random(2..8#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a4", "description": ""}}, "metadata": {"description": "<p>Product rule</p>", "licence": "Creative Commons Attribution 4.0 International"}, "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/"}]}