// Numbas version: finer_feedback_settings
{"name": "cormac's copy of cormac's copy of Blathnaid's copy of Implicit differentiation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "statement": "<p>Given the following relation between $x$ and $y$<br/>\\[\\simplify[all,!collectNumbers]{x^2+y^2+{a}x+{b}y}=\\var{c}\\]<br/>answer the following question.</p>", "name": "cormac's copy of cormac's copy of Blathnaid's copy of Implicit differentiation", "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"c": {"name": "c", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(1..9)"}, "a": {"name": "a", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "-random(1..9)"}, "b": {"name": "b", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "random(1..9)"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "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"}, "rulesets": {}, "advice": "<p>On differentiating both sides of the equation implicitly we get<br/>\\[2x + \\simplify[all,!collectNumbers]{2y*Diff(y,x,1) + {a} + {b} *Diff(y,x,1)} = 0\\]<br/>Collecting terms in $\\displaystyle\\frac{dy}{dx}$ and rearranging the equation we get <br/>\\[(\\var{b} + 2y) \\frac{dy}{dx} = \\simplify[all,!collectNumbers]{{ -a} -2x}\\] and hence on further rearranging:<br/>\\[\\frac{dy}{dx} = \\simplify[all,!collectNumbers]{({ - a} - 2 * x) / ({b} + (2 * y))}\\]</p>", "tags": [], "extensions": [], "parts": [{"gaps": [{"expectedvariablenames": [], "scripts": {}, "variableReplacementStrategy": "originalfirst", "answer": "(({( - a)} + ( - (2 * x))) / ({b} + (2 * y)))", "checkvariablenames": false, "showpreview": true, "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "marks": "5", "type": "jme", "answersimplification": "all,!collectNumbers", "variableReplacements": [], "showFeedbackIcon": true, "checkingtype": "absdiff", "vsetrangepoints": 5}], "marks": 0, "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "prompt": "\n      <p>Using implicit differentiation find $\\displaystyle \\frac{dy}{dx}$&nbsp;in terms of $x$ and $y$.</p>\n        <p>Input your answer here:</p>\n        <p>$\\displaystyle \\frac{dy}{dx}= $ [[0]]</p>\n      ", "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true}], "variable_groups": [], "ungrouped_variables": ["a", "c", "b"], "type": "question", "contributors": [{"name": "cormac breen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/306/"}]}]}], "contributors": [{"name": "cormac breen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/306/"}]}