// Numbas version: exam_results_page_options
{"name": "Chain rule 4", "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"], "name": "Chain rule 4", "tags": [], "preamble": {"css": "", "js": ""}, "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>", "rulesets": {}, "parts": [{"prompt": "<p>\\(\\frac{df}{dx}=\\)[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({a1}*{a2}*{a3}x^{{a3}-1})({a2}x^{{a3}}+{a4})^{{a1}-1}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "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>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a1": {"definition": "random(2..8#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "random(1..4#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(2..6#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a4": {"definition": "random(1..14#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a4", "description": ""}}, "metadata": {"description": "<p>Chain 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/"}]}