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