// Numbas version: finer_feedback_settings
{"name": "DOCE UNO 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", "s2", "s1", "det", "c1"], "name": "DOCE UNO 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[std]{u = ({a}x+{b})}\\Rightarrow \\simplify[std]{Diff(u,x,1) = {a}}\\]</p>\n<p>\\[\\simplify[std]{v = ({c} * x^2+{d})} \\Rightarrow \\simplify[std]{Diff(v,x,1) = {2*c}x}\\]</p>\n<p>Ahora sustituimos en la f&oacute;rmula del cociente:</p>\n<p>\\[\\begin{eqnarray*} \\frac{df}{dx}&amp;=&amp;\\simplify[std]{({a}({c}x^2+{d})-{2*c}x({a}x+{b}))/({c}x^2+{d})^2}\\\\ &amp;=&amp;\\simplify[std]{({a*c}x^2+{a*d}-{2*c*a}x^2-{2*c*b}x)/({c}x^2+{d})^2}\\\\ &amp;=&amp;\\simplify[std]{({-c*a}x^2+{-2*b*c}x+{a*d})/({c}x^2+{d})^2} \\end{eqnarray*}\\]</p>\n<p>Con lo cual se concluye que&nbsp;$g(x)=\\simplify[std]{{-c*a}x^2+{-2*b*c}x+{a*d}}$</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"stepsPenalty": 0, "prompt": "<p>\\[\\simplify[std]{f(x) = ({a} * x+{b})/({c}x^2+{d})}\\]<br/>La derivada tiene la forma:&nbsp;\\[\\frac{df}{dx}=\\simplify[std]{g(x)/({c}x^2+{d})^2}\\]<br/>Cu&aacute;l es el polinomio $g(x)$, 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>$v=\\simplify[std]{{c}x^2+{d}}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"notallowed": {"message": "<p>Input all numbers as fractions or integers and not as decimals.</p>", "showStrings": false, "strings": ["."], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{-c*a}x^2+{-2*b*c}x+{a*d}", "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(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "if(a*d=b*c1,c1+1,c1)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "s1*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "s2*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "s2": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s2", "description": ""}, "s1": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "det": {"definition": "a*d-b*c", "templateType": "anything", "group": "Ungrouped variables", "name": "det", "description": ""}, "c1": {"definition": "random(1..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}}, "metadata": {"description": "<p>The derivative of $\\displaystyle \\frac{ax+b}{cx^2+d}$ is of the form $\\displaystyle \\frac{g(x)}{(cx^2+d)^2}$. Find $g(x)$.</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/"}]}