// Numbas version: exam_results_page_options
{"name": "Derivada aplicando la regla del cociente", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Derivada aplicando la regla del cociente", "tags": [], "metadata": {"description": "<div class=\"tlid-input input has-transliteration\">\n<div class=\"source-wrap\">\n<div class=\"input-full-height-wrapper tlid-input-full-height-wrapper\">\n<div class=\"source-input\">\n<div class=\"source-header\">\n<div class=\"go-wrap\"></div>\n</div>\n<div class=\"source-footer-wrap source-or-target-footer\">\n<div class=\"source-input-tools\" id=\"gt-input-tool\">\n<div id=\"itamenu\"></div>\n</div>\n<div class=\"source-footer\">\n<div class=\"src-tts left-positioned ttsbutton jfk-button-flat source-or-target-footer-button jfk-button\" aria-label=\"Escuchar\" data-tooltip=\"Escuchar\" aria-pressed=\"false\" role=\"button\" data-tooltip-align=\"t,c\" aria-hidden=\"false\" aria-disabled=\"false\" tabindex=\"0\">Diferenciar&nbsp; $\\displaystyle \\frac{ax+b}{cx+d}$.</div>\n</div>\n</div>\n</div>\n</div>\n</div>\n</div>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p><span style=\"vertical-align: inherit;\"><span style=\"vertical-align: inherit;\">Derivar la siguiente funci&oacute;n $ f (x) $ usando la regla del cociente.</span></span></p>", "advice": "<p>La regla del cociente dice 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>\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 = ({c} * x+{d})} \\Rightarrow \\simplify[std]{Diff(v,x,1) = {c}}\\]</p>\n<p>Por lo tanto, al sustituir en la regla del cociente anterior obtenemos:</p>\n<p>\\[\\begin{eqnarray*} \\frac{df}{dx}&amp;=&amp;\\simplify[std]{({a}({c}x+{d})-{c}({a}x+{b}))/({c}x+{d})^2}\\\\ &amp;=&amp;\\simplify[std]{({a*c}x+{a*d}-{c*a}x-{c*b})/({c}x+{d})^2}\\\\ &amp;=&amp;\\simplify[std]{{det}/({c}x+{d})^2} \\end{eqnarray*}\\]</p>", "rulesets": {"surdf": [{"result": "(sqrt(b)*a)/b", "pattern": "a/sqrt(b)"}], "std": ["all", "!collectNumbers", "fractionNumbers"]}, "extensions": [], "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "s1*random(1..9)", "description": "", "templateType": "anything"}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "random(1..8)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "if(a*d=b*c1,c1+1,c1)", "description": "", "templateType": "anything"}, "s1": {"name": "s1", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything"}, "det": {"name": "det", "group": "Ungrouped variables", "definition": "a*d-b*c", "description": "", "templateType": "anything"}, "s2": {"name": "s2", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "templateType": "anything"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "s2*random(1..9)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "c", "b", "d", "s2", "s1", "det", "c1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "\n\t\t\t<p>\\[\\simplify[std]{f(x) = ({a} * x+{b})/({c}*x+{d})}\\]</p>\n\t\t\t      <p>$\\displaystyle \\frac{df}{dx}=\\;$[[0]]</p>\n\t\t\t", "stepsPenalty": 1, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p>La regla del cociente dice 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>"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 3, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{det}/({c}x+{d})^2", "answerSimplification": "std", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [10, 11], "checkVariableNames": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "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/"}]}