// Numbas version: exam_results_page_options
{"name": "Standard Differentiation (Trig2)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Standard Differentiation (Trig2)", "tags": [], "metadata": {"description": "<p>Differentiate $f(x) = ax^m$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Differentiate the following trigonometric function $f(x)$ using the&nbsp;standard rules.</p>", "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>", "rulesets": {"surdf": [{"pattern": "a/sqrt(b)", "result": "(sqrt(b)*a)/b"}], "std": ["all", "!collectNumbers", "!collectNumbers", "fractionNumbers", "fractionNumbers", "all", "all"]}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"m": {"name": "m", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-9..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "m"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\displaystyle \\simplify[std]{f(x) = {a}cos({m}x) }$</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>", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "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>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-{a*m}sin({m}x)", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "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/"}]}