// Numbas version: exam_results_page_options
{"name": "CINCO UNO Derivada producto", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["c", "p", "c1"], "name": "CINCO UNO Derivada producto", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$\\dfrac{d}{dx}\\left [\\simplify{(x+{c[0]})(x+{c1})}\\right ]$=[[0]]</p>\n<p><code>Ejemplo de respuesta: si la respuesta es </code>$-7x^5+7x^3-8x$,<code> digite $-7x^5+7x^3-8x en la barra de respuesta.</code></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>En este ejercicio se debe emplear la regla del producto.</p>\n<p>$\\dfrac{dy}{dx}=v\\dfrac{du}{dx}+u\\dfrac{dv}{dx}$ con $y=uv$.</p>\n<p>En la funci&oacute;n $y=\\simplify{(x+{c[0]})(x+{c1})}$, podemos identificar que $u=(\\simplify{x+{c[0]}})$ y $v=(\\simplify{x+{c1}})$.</p>\n<p>Derivamos con respecto a&nbsp;$x$, con lo cual se obtiene:</p>\n<p>$\\dfrac{du}{dx}=1$ y $\\dfrac{dv}{dx}=1$.</p>\n<p>Reemplazamos en la f&oacute;rmula,&nbsp;$\\dfrac{dy}{dx}=v\\dfrac{du}{dx}+u\\dfrac{dv}{dx}$ con $y=uv$, es decir: $\\dfrac{dy}{dx}=1(\\simplify{x+{c1}})+1(\\simplify{x+{c[0]}})$</p>\n<p>Luego de simplificar se llega a que la derivada es: $\\dfrac{dy}{dx}=\\simplify{2x+{c[0]}+{c1}}$</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, "scripts": {}, "answer": "2x+{c1}+{c[0]}", "marks": "25", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{d}{dx}\\left [\\simplify{({c[2]}x+{c[3]})({c[4]}x+{c[5]})}\\right ]$=[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({c[2]}{c[4]}*2x)+({c[3]}{c[4]}+{c[2]}{c[5]})", "marks": "25", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{d}{dx}\\left [\\simplify{(x^2+{c[6]})({c[7]}x+{c[8]})}\\right ]$=[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "({c[7]}*3x^2)+(2{c[8]}x)+({c[7]}{c[6]})", "marks": "25", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{d}{dx}\\left [\\simplify{(x^2+{c[9]})(x^3+{c[10]})}\\right ]$=[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "5x^4+3{c[9]}x^2+2{c[10]}x", "marks": "25", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Calcular la derivada de cada una de las siguientes funciones.</p>", "variable_groups": [], "variablesTest": {"maxRuns": "187", "condition": "\n"}, "variables": {"p": {"definition": "repeat(random(2..6),10)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "c": {"definition": "repeat(random(-9..9 except 0),11)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "c1": {"definition": "random(-9..9 except 0 except c[0])", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}}, "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "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/"}]}