// Numbas version: finer_feedback_settings
{"name": "Implicit differentiation (1)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "variable_groups": [], "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"}, "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "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>", "variables": {"a": {"templateType": "anything", "description": "", "definition": "-random(1..9)", "name": "a", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "description": "", "definition": "random(1..9)", "name": "c", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "description": "", "definition": "random(1..9)", "name": "b", "group": "Ungrouped variables"}}, "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>", "extensions": [], "functions": {}, "name": "Implicit differentiation (1)", "ungrouped_variables": ["a", "c", "b"], "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "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      ", "type": "gapfill", "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "gaps": [{"answer": "(({( - a)} + ( - (2 * x))) / ({b} + (2 * y)))", "vsetrange": [0, 1], "marks": 2, "scripts": {}, "checkingaccuracy": 0.001, "variableReplacements": [], "vsetrangepoints": 5, "expectedvariablenames": [], "showCorrectAnswer": true, "type": "jme", "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "showFeedbackIcon": true, "showpreview": true, "answersimplification": "all,!collectNumbers"}], "showFeedbackIcon": true}], "preamble": {"css": "", "js": ""}, "type": "question", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}]}], "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}