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{"name": "Musa's copy of 3 Differentiation - Trigonometric Functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Musa's copy of 3 Differentiation - Trigonometric Functions", "tags": [], "metadata": {"description": "<p>More work on differentiation with&nbsp;trigonometric functions</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><strong>Differentiate the following&nbsp;trigonometric functions using the chain rule.</strong></p>\n<p>Do not write out $dy/dx$; only input the differentiated right hand side of each equation.</p>", "advice": "<p><strong></strong>If you don't know how to differentiate trigonometric functions, please see&nbsp;<em>'Differentiation 4 - Trigonometric Functions'</em>.</p>\n<p><strong></strong></p>\n<p><strong>These questions use the chain rule.</strong></p>\n<p>The earlier questions are easy to do by inspection, e.g using Part a:</p>\n<p style=\"text-align: center;\">$y=sin(\\var{c[0]}x)$.</p>\n<p>We differentiate the term(s) inside the function, here the term is $\\var{c[0]}x$.</p>\n<p>Then we derive $sin$ of any function, giving us $cos$.</p>\n<p>Putting our results together, we get</p>\n<p>$\\var{c[0]}cos(\\var{c[0]}x)$.</p>", "rulesets": {}, "extensions": [], "variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "shuffle(2..8)[0..5]", "description": "<p>coefficients</p>", "templateType": "anything"}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "repeat(random(3..6),2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["c", "p"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>$y=-5\\cos(\\var{c[3]}x)+\\sin(\\var{c[4]}x)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "5{c[3]}sin({c[3]}x)+{c[4]}cos({c[4]}x)", "answerSimplification": "all", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Kevin Bohan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3363/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Kevin Bohan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3363/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}