// Numbas version: finer_feedback_settings
{"name": "CATORCE UNO Derivacion implicita", "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"], "name": "CATORCE UNO Derivacion implicita", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Empleando derivaci&oacute;n impl&iacute;cita em ambos lados de la expresi&oacute;n, se obtiene:&nbsp;</p>\n<p>\\[2x + \\simplify[all,!collectNumbers]{2y*Diff(y,x,1) + {a} + {b} *Diff(y,x,1)} = 0\\]<br/>Tomando factor com&uacute;n&nbsp;$\\displaystyle\\frac{dy}{dx}$&nbsp;y reordenando t&eacute;rminos&nbsp;<br/>\\[(\\var{b} + 2y) \\frac{dy}{dx} = \\simplify[all,!collectNumbers]{{ -a} -2x}\\] por &uacute;ltimo, se despeja&nbsp;$\\displaystyle\\frac{dy}{dx}$:<br/>\\[\\frac{dy}{dx} = \\simplify[all,!collectNumbers]{({ - a} - 2 * x) / ({b} + (2 * y))}\\]</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\displaystyle \\frac{dy}{dx}= $ [[0]]</p>\n<p><code>Ejemplo de respuesta: Digite (7&minus;2x)/(9+2y) si la respuesta es</code>$\\dfrac{7-2x}{9+dy}$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all,!collectNumbers", "scripts": {}, "answer": "(({( - a)} + ( - (2 * x))) / ({b} + (2 * y)))", "marks": "20", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>Dada la funci&oacute;n impl&iacute;cita en las variables&nbsp;$x$ y&nbsp;$y$<br/>\\[\\simplify[all,!collectNumbers]{x^2+y^2+{a}x+{b}y}=\\var{c}\\]<br/>Calcular$\\displaystyle \\frac{dy}{dx}$ usando derivaci&oacute;n impl&iacute;cita, exprese la respuesta en t&eacute;rminos de&nbsp;$x$ y&nbsp;$y$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "-random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"description": "\n                            \t\t<p>Implicit differentiation.</p>\n                            \t\t<p>Given $x^2+y^2+ax+by=c$ find $\\displaystyle \\frac{dy}{dx}$ in terms of $x$ and $y$.</p>\n                            \t\t<p>&nbsp;</p>\n                            \t\t", "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/"}]}