// Numbas version: exam_results_page_options
{"name": "DOCE DOS Derivadas cociente", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "s1", "d1"], "name": "DOCE DOS Derivadas cociente", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Si&nbsp;$u$ y&nbsp;$v$ son funciones derivables de&nbsp;$x$,&nbsp;entonces se cumple que:<br/>\\[\\simplify[std]{Diff(u/v,x,1) = (v * Diff(u,x,1) - u * Diff(v,x,1))/v^2}\\]</p>\n<p>Para el ejemplo, tenemos que:</p>\n<p>\\[\\simplify[dPoly]{u = {a} * x + {b}}\\Rightarrow \\simplify{Diff(u,x,1) = {a}}\\]</p>\n<p>\\[\\simplify[dPoly]{v = Sqrt({c} * x + {d})} \\Rightarrow \\simplify[dPoly]{Diff(v,x,1) = {c} / (2 * Sqrt({c} * x + {d}))}\\]</p>\n<p>Ahora sustituimos en la f&oacute;rmula del cociente:</p>\n<p>\\[\\simplify[dPoly]{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>Con lo cual se concluye que&nbsp;&nbsp;\\[\\simplify[dPoly]{g(x) = {a * c} * x + {2 * a * d -(c * b)}}\\].</p>", "rulesets": {"std": ["all", "!collectNumbers"], "dpoly": ["std", "fractionNumbers"]}, "parts": [{"stepsPenalty": "0", "prompt": "<p>\\[\\simplify[dPoly]{f(x) = ({a} * x + {b}) / Sqrt({c} * x + {d})}\\]</p>\n<p>La derivada tiene la forma: &nbsp;\\[\\simplify[dPoly]{Diff(f,x,1) = g(x) / (2 * ({c} * x + {d}) ^ (3 / 2))}\\]</p>\n<p>Cu&aacute;l es el polinomio&nbsp;$g(x)$,&nbsp;con el que la derivada es la correcta.</p>\n<p>$g(x)=\\;$[[0]]</p>\n<p><code>Ejemplo de respuesta: escriba &minus;21x^2&minus;12x+7, si la respuesta es </code>$&minus;21x^2&minus;12x+7$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Si&nbsp;$u$ y&nbsp;$v$ son funciones derivables de&nbsp;$x$,&nbsp;entonces se cumple que:<br/>\\[\\simplify[std]{Diff(u/v,x,1) = (v * Diff(u,x,1) - u * Diff(v,x,1))/v^2}\\]</p>\n<p>con:</p>\n<p>$u=\\simplify[std]{{a} * x+{b}}$</p>\n<p>$v=\\simplify[std]{Sqrt({c} * x + {d})}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "dPoly", "scripts": {}, "answer": "(({(a * c)} * x) + {((2 * a * d) + ( - (c * b)))})", "marks": "50", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Calcular la derivada de la funci&oacute;n</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1,3,5,7)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "if(2|a,random(-7..7#2),random(-8..8#2))", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "if(a*d1=b*c,abs(d1)+1,d1)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "s1": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "d1": {"definition": "s1*random(1..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "d1", "description": ""}}, "metadata": {"description": "<p>Differentiate $f(x) = (a x + b)/ \\sqrt{c x + d}$ and find $g(x)$ such that $ f^{\\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}]}], "contributors": [{"name": "Marlon Arcila", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/321/"}]}