// Numbas version: exam_results_page_options
{"name": " Chain rule 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p>\\(f(x)=\\var{a1}sin(\\var{a2}x^{\\var{a3}}+\\var{a4})\\)</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)=\\var{a1}sin(u)\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{du}=\\var{a1}cos(u)\\) &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}cos(u).\\simplify{{a2}*{a3}x^{{a3}-1}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\frac{df}{dx}=\\simplify{{a1}*{a2}*{a3}x^{{a3}-1}}cos(\\var{a2}x^{\\var{a3}}+\\var{a4})\\)</p>", "functions": {}, "statement": "<p>Differentiate the function:</p>\n<p style=\"padding-left: 30px;\">\\(f(x)=(\\var{a2}x^{\\var{a3}}+\\var{a4})^\\var{a1}\\)</p>", "rulesets": {}, "variables": {"a1": {"group": "Ungrouped variables", "name": "a1", "definition": "random(2..7#1)", "templateType": "randrange", "description": ""}, "a3": {"group": "Ungrouped variables", "name": "a3", "definition": "random(3..6#1)", "templateType": "randrange", "description": ""}, "a4": {"group": "Ungrouped variables", "name": "a4", "definition": "random(3..12#1)", "templateType": "randrange", "description": ""}, "a2": {"group": "Ungrouped variables", "name": "a2", "definition": "random(2..6#1)", "templateType": "randrange", "description": ""}}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "tags": [], "ungrouped_variables": ["a1", "a2", "a3", "a4"], "metadata": {"description": "<p>Chain rule</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"type": "gapfill", "variableReplacements": [], "showFeedbackIcon": true, "gaps": [{"type": "jme", "variableReplacements": [], "showpreview": true, "checkvariablenames": false, "showCorrectAnswer": false, "checkingaccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "vsetrange": [0, 1], "scripts": {}, "expectedvariablenames": [], "checkingtype": "absdiff", "answersimplification": "all", "answer": "{a1}*{a2}*{a3}x^({a3}-1)({a2}x^{a3}+{a4})^{{a1}-1}", "vsetrangepoints": 5, "showFeedbackIcon": true, "marks": "5"}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>\\(\\frac{df}{dx}=\\)&nbsp;[[0]]</p>", "scripts": {}, "marks": 0}], "extensions": [], "variablesTest": {"condition": "", "maxRuns": 100}, "name": " Chain rule 3", "type": "question", "contributors": [{"name": "Milena Venkova", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2169/"}]}]}], "contributors": [{"name": "Milena Venkova", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2169/"}]}