// Numbas version: exam_results_page_options
{"name": "Standard Differentiation (Trig)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<p>Differentiate the following trigonometric function $f(x)$ using the&nbsp;standard rules.</p>", "preamble": {"css": "", "js": ""}, "tags": [], "rulesets": {"surdf": [{"pattern": "a/sqrt(b)", "result": "(sqrt(b)*a)/b"}], "std": ["all", "!collectNumbers", "fractionNumbers"]}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>The standard rule for differentiation of polynomial expressions is</p>\n<p>\\[f(x) = ax^n\\]<br/>\\[\\frac{d(f(x))}{dx}=anx^{n-1}\\]</p>\n<p>For this example...</p>", "extensions": [], "name": "Standard Differentiation (Trig)", "functions": {}, "ungrouped_variables": ["a", "m"], "parts": [{"scripts": {}, "steps": [{"unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "marks": 0, "showCorrectAnswer": true, "prompt": "<p>The standard rule for differentiation of trigonometric expressions is</p>\n<p>\\[f(x) = a \\sin{nx}\\]<br/>\\[\\frac{d(f(x))}{dx}=an\\cos{nx}\\]</p>", "type": "information", "scripts": {}}], "customMarkingAlgorithm": "", "gaps": [{"failureRate": 1, "checkVariableNames": false, "vsetRange": [0, 1], "checkingType": "absdiff", "answer": "{a*m}cos({m}x)", "answerSimplification": "std", "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "scripts": {}, "showFeedbackIcon": true, "variableReplacements": [], "vsetRangePoints": 5, "checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "unitTests": [], "expectedVariableNames": [], "marks": "2", "showCorrectAnswer": true, "showPreview": true, "type": "jme"}], "extendBaseMarkingAlgorithm": true, "prompt": "<p>$\\displaystyle \\simplify[std]{f(x) = {a}sin({m}x) }$</p>\n<p>$\\displaystyle \\frac{df}{dx}=\\;$[[0]]</p>\n<p>Clicking on Show steps gives you more information, you will not lose any marks by doing so.</p>", "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "unitTests": [], "stepsPenalty": 0, "marks": 0, "showCorrectAnswer": true, "type": "gapfill", "sortAnswers": false}], "metadata": {"description": "<p>Differentiate $f(x) = ax^m$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"a": {"name": "a", "description": "", "templateType": "anything", "definition": "random(-9..9)", "group": "Ungrouped variables"}, "m": {"name": "m", "description": "", "templateType": "anything", "definition": "random(1..9)", "group": "Ungrouped variables"}}, "type": "question", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}, {"name": "Heather Driscoll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1703/"}, {"name": "Johnny Yi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2810/"}]}]}], "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}, {"name": "Heather Driscoll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1703/"}, {"name": "Johnny Yi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2810/"}]}