// Numbas version: finer_feedback_settings
{"name": "Derivative of polynomial \u2013 bug?", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Derivative of polynomial \u2013 bug?", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<p>Given the function \\[f(x)=\\var{f1},\\]</p>", "advice": "<p>Rewrite function \\(f(x)\\) as</p>\n<p>\\(\\simplify{{a}x^({power_a})+{b} x^({power_b})+{c}*x^({power_c})+{d}*x^({power_d})}\\)</p>\n<p></p>\n<p>Use the rules of differentiation and the table of derivatives:</p>\n<p>\\((f(x)+g(x))'=f'(x)+g'(x);\\)</p>\n<p>\\((c\\times f(x))'=c\\times&nbsp;f'(x),\\) where \\(c\\) is a constant;</p>\n<p>\\((c)'=0,\\)&nbsp;where \\(c\\) is a constant;</p>\n<p>\\((x^n)'=nx^{n-1},\\)&nbsp;where \\(c\\) is a constant.</p>\n<p>The final answer is:</p>\n<p>\\(f'=\\simplify{{df1}}\\)</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "f1", "definition": "random([2, 4])/random([3, 5, 7, 9, 11, 13])", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "f1", "definition": "random([2, 4])/random([3, 5, 7, 9, 11, 13])", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "f1", "definition": "-random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "power_a": {"name": "power_a", "group": "f1", "definition": "-random(5..12)", "description": "", "templateType": "anything", "can_override": false}, "power_b": {"name": "power_b", "group": "f1", "definition": "-random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "f1": {"name": "f1", "group": "f1", "definition": "simplify(expression(\"{a}/x^({-power_a})+{b}/x^({-power_b})+{c}*x^({power_c})+{d}*sqrt(x^({power_d_prm}))\"), \"all\")", "description": "", "templateType": "anything", "can_override": false}, "df1": {"name": "df1", "group": "f1", "definition": "simplify(expression(\"{a*power_a}*x^({power_a-1})+{b*power_b}*x^({power_b-1})+{c}*{power_c}*x^({power_c-1})+{d*power_d}*x^({power_d-1})\"), \"basic\")", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "f1", "definition": "-random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "power_c": {"name": "power_c", "group": "f1", "definition": "random(2..3)", "description": "", "templateType": "anything", "can_override": false}, "power_d": {"name": "power_d", "group": "f1", "definition": "power_d_prm/2", "description": "", "templateType": "anything", "can_override": false}, "power_d_prm": {"name": "power_d_prm", "group": "f1", "definition": "random([3, 5, 7, 9, 11, 13])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "f1", "variables": ["a", "power_a", "b", "power_b", "c", "power_c", "d", "power_d_prm", "power_d", "f1", "df1"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Find the derivative \\(\\frac{df}{dx}=\\)</p>", "answer": "{df1}", "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": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}]}], "contributors": [{"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}