// Numbas version: exam_results_page_options
{"name": "Regla del cociente - Derivada de una funci\u00f3n lineal sobre la funci\u00f3n ra\u00edz", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "parts": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>\\[\\simplify[std]{f(x) = ({a} * x + {b}) / Sqrt({c} * x + {d})}\\]</p>\n<p>Se da la relaci&oacute;n: \\[\\simplify[std]{Diff(f,x,1) = g(x) / (2 * ({c} * x + {d}) ^ (3 / 2))}\\]</p>\n<p>para el polinomio $g(x)$. Encontrar $g(x)$.</p>\n<p></p>\n<p>Ingresa todos los n&uacute;meros como fracciones o enteros.</p>\n<p>Puede hacer clic en Mostrar pasos para obtener ayuda.&nbsp;</p>\n<p></p>\n<p>$g(x)=\\;$[[0]]</p>", "marks": 0, "showFeedbackIcon": true, "unitTests": [], "variableReplacements": [], "steps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "information", "showCorrectAnswer": true, "prompt": "<p>La regla del cociente indica que si $u$ y $v$ son funciones de $x$, entonces<br/>\\[\\simplify[std]{Diff(u/v,x,1)=(v * Diff(u,x,1) -(u * Diff(v,x,1))) / v^2}\\]</p>", "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": []}], "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "gaps": [{"scripts": {}, "extendBaseMarkingAlgorithm": true, "type": "jme", "showCorrectAnswer": true, "expectedVariableNames": [], "marks": 3, "showFeedbackIcon": true, "unitTests": [], "variableReplacements": [], "failureRate": 1, "checkingType": "absdiff", "checkVariableNames": false, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "answerSimplification": "all", "notallowed": {"partialCredit": 0, "message": "<p>Input all numbers as fractions or integers.</p>", "showStrings": false, "strings": ["."]}, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "showPreview": true, "answer": "(({(a * c)} * x) + {((2 * a * d) + ( - (c * b)))})"}], "stepsPenalty": 0, "customMarkingAlgorithm": ""}], "preamble": {"js": "", "css": ""}, "functions": {}, "advice": "<p>La regla del cociente dice que si $u$ y $v$ son funciones de $x$, entonces</p>\n<p>\\[\\simplify[std]{Diff(u/v,x,1)=(v * Diff(u,x,1) -(u * Diff(v,x,1))) / v ^ 2}\\]</p>\n<p>Para este ejemplo:</p>\n<p>\\[\\simplify[std]{u = {a} * x + {b}}\\Rightarrow \\simplify[std]{Diff(u,x,1) = {a}}\\]</p>\n<p>\\[\\simplify[std]{v = Sqrt({c} * x + {d})} \\Rightarrow \\simplify[std]{Diff(v,x,1) = {c} / (2 * Sqrt({c} * x + {d}))}\\]</p>\n<p>Por lo tanto, al sustituir en la regla del cociente anterior obtenemos:</p>\n<p>\\[\\simplify[std]{Diff(f,x,1) = ({a} * Sqrt({c} * x + {d}) -(({a} * x + {b}) * Diff(v,x,1))) / ({c} * x + {d}) = ({a} * Sqrt({c} * x + {d}) -(({c} * ({a} * x + {b})) / (2 * Sqrt({c} * x + {d})))) / ({c} * x + {d}) = ({2 * a} * ({c} * x + {d}) -({c} * ({a} * x + {b}))) / (2 * ({c} * x + {d}) ^ (3 / 2)) = ({a * c} * x + {2 * a * d -(c * b)}) / (2 * ({c} * x + {d}) ^ (3 / 2))}\\]</p>\n<p>Por lo tanto \\[\\simplify[std]{g(x) = {a * c} * x + {2 * a * d -(c * b)}}\\].</p>", "metadata": {"description": "<p>La derivada de $\\displaystyle \\frac{ax+b}{\\sqrt{cx+d}}$ is $\\displaystyle \\frac{g(x)}{2(cx+d)^{3/2}}$. Encontrar $g(x)$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "extensions": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>Derivar la siguiente funci&oacute;n $ f (x) $ usando la regla del cociente o de otra manera.</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "name": "Regla del cociente - Derivada de una funci\u00f3n lineal sobre la funci\u00f3n ra\u00edz", "ungrouped_variables": ["a", "c", "b", "d", "s1", "d1"], "variables": {"b": {"name": "b", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "if(2|a,random(-7..7#2),random(-8..8#2))"}, "d1": {"name": "d1", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "s1*random(1..8)"}, "c": {"name": "c", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,3,5,7)"}, "s1": {"name": "s1", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)"}, "a": {"name": "a", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..8)"}, "d": {"name": "d", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "if(a*d1=b*c,abs(d1)+1,d1)"}}, "variable_groups": [], "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}