// Numbas version: exam_results_page_options
{"name": "Implicit 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "-random(1..9)", "description": "", "templateType": "anything"}}, "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>", "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "name": "Implicit 1", "parts": [{"customMarkingAlgorithm": "", "useCustomName": false, "scripts": {}, "marks": 0, "variableReplacements": [], "gaps": [{"checkingType": "absdiff", "useCustomName": false, "answerSimplification": "all,!collectNumbers", "marks": 2, "checkingAccuracy": 0.001, "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "checkVariableNames": false, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "type": "jme", "showFeedbackIcon": true, "customMarkingAlgorithm": "", "valuegenerators": [{"name": "x", "value": ""}, {"name": "y", "value": ""}], "showPreview": true, "scripts": {}, "variableReplacements": [], "customName": "", "unitTests": [], "answer": "(({( - a)} + ( - (2 * x))) / ({b} + (2 * y)))", "variableReplacementStrategy": "originalfirst"}], "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true, "customName": "", "sortAnswers": false, "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        \n      \n      ", "unitTests": [], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showFeedbackIcon": true}], "rulesets": {}, "variable_groups": [], "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>", "metadata": {"description": "\n    \t\t        \t\t                    \t\t<p>Implicit differentiation.</p>\n    \t\t        \t\t                    \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        \t\t                    \t\t<p>&nbsp;</p>\n    \t\t        \t\t                    \n    \t\t        \n    \t\t", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "ungrouped_variables": ["c", "a", "b"], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}