// Numbas version: exam_results_page_options
{"name": "CINCO DOS 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"], "name": "CINCO DOS Derivada producto", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>$\\dfrac{d}{dx}\\left [&nbsp;\\simplify{x^2(x+{c[0]})^{p[0]}}\\right ]$=[[0]]</p>\n<p><code>Escriba la respuesta con la siguiente forma&nbsp;</code>$3x(4x+2)^2+6x^2(x+2)$</p>\n<p><code>para lo cual debe digitar 3x(4x+2)^2+6x^2(x+2), en la respuesta.</code></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Adem&aacute;s de las reglas b&aacute;sicas de derivaci&oacute;n, en este ejercicio se deben aplicar las reglas del producto y regla de la cadena.</p>\n<p>Regla del producto&nbsp;$\\dfrac{d}{dx}[f \\times g]=f \\times g'+g \\times f'$ con:</p>\n<p>$f=x^2$</p>\n<p>$g=\\simplify{(x+{c[0]})^{p[0]}}$, pero esta funci&oacute;n $g$ es compuesta, en ella se identifican:</p>\n<p>funci&oacute;n externa: $g(u)=\\simplify{u^{p[0]}}$</p>\n<p>funci&oacute;n interna: $u=\\simplify{x+{c[0]}}$</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": "all", "scripts": {}, "answer": "2x*(x+{c[0]})^{p[0]}+{p[0]}x^2*(x+{c[0]})^({p[0]}-1)", "marks": "20", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{d}{dx}\\left [&nbsp;\\simplify{{c[1]}x^3({c[2]}x+{c[3]})^{p[1]}}\\right ]$=[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "3{c[1]}x^2*({c[2]}x+{c[3]})^{p[1]}+{p[1]}{c[2]}{c[1]}x^3*({c[2]}x+{c[3]})^({p[1]}-1)", "marks": "20", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{d}{dx}\\left [&nbsp;\\simplify{{c[4]}x^{p[2]}({c[5]}x^2+{c[6]})^{p[3]}}\\right ]$=[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{p[2]}{c[4]}x^({p[2]}-1)*({c[5]}x^2+{c[6]})^{p[3]}+2{p[3]}{c[4]}{c[5]}x^({p[2]}+1)*({c[5]}x^2+{c[6]})^({p[3]}-1)", "marks": "20", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{d}{dx}\\left [&nbsp;\\simplify{(x+{c[7]})^{p[4]}(x+{c[8]})^{p[5]}}\\right ]$=[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{p[4]}(x+{c[7]})^({p[4]}-1)*(x+{c[8]})^{p[5]}+{p[5]}(x+{c[8]})^({p[5]}-1)*(x+{c[7]})^{p[4]}", "marks": "20", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\dfrac{d}{dx}\\left [&nbsp;\\simplify{({c[9]}x^2+{c[10]})^{p[6]}({c[11]}x^2+{c[12]})^{p[7]}}\\right ]$=[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "2{p[6]}{c[9]}x*({c[9]}x^2+{c[10]})^({p[6]}-1)*({c[11]}x^2+{c[12]})^{p[7]}+2{p[7]}{c[11]}x*({c[11]}x^2+{c[12]})^({p[7]}-1)*({c[9]}x^2+{c[10]})^{p[6]}", "marks": "20", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Calcular la derivada de las siguientes funciones, empleando la regla de la cadena.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"p": {"definition": "repeat(random(2..6),10)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "c": {"definition": "repeat(random(-9..9 except 0),13)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}}, "metadata": {"description": "<p>Using the chain rule within product rule problems</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/"}]}