// Numbas version: exam_results_page_options {"name": "T6Q12 (custom feedback)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "variables": {}, "metadata": {"description": "

Partial differentiation question with customised feedback to catch some common errors.

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$\\frac{\\partial z}{\\partial x}=$ []

", "sortAnswers": false, "showCorrectAnswer": true, "gaps": [{"vsetRangePoints": 5, "scripts": {}, "vsetRange": [0, 1], "customMarkingAlgorithm": "malrules:\n [\n [\"-1/sqrt(y^2-x^2)\", \"Check the rule for differentiating $\\\\sin^{-1} \\\\left( \\\\cdot \\\\right)$.\"],\n [\"1/sqrt(y^2+x^2)\", \"Check the rule for differentiating $\\\\sin^{-1} \\\\left( \\\\cdot \\\\right)$.\"],\n [\"y/(y^2+x^2)\", \"Check the rule for differentiating $\\\\sin^{-1} \\\\left( \\\\cdot \\\\right)$.\"]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x),\"feedback\":x],\n x,\n malrules\n )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n map(\n len(filter(not x ,x,map(\n try(\n resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n message,\n false\n ),\n vars,\n vset\n )))$\\frac{\\partial z}{\\partial y}=$ []

", "sortAnswers": false, "showCorrectAnswer": true, "gaps": [{"vsetRangePoints": 5, "scripts": {}, "vsetRange": [0, 1], "customMarkingAlgorithm": "malrules:\n [\n [\"1/sqrt(1-(x/y)^2)\", \"Don't forget to multiply by the derivative of the top. Recall that $\\\\frac{\\\\partial}{\\\\partial y} \\\\left( \\\\sin^{-1} \\\\left( \\\\frac{y}{a} \\\\right) \\\\right) = \\\\frac{1}{\\\\sqrt{a^2-y^2}}$ but $\\\\frac{\\\\partial}{\\\\partial y} \\\\left( \\\\sin^{-1} \\\\left( \\\\frac{f(y)}{a} \\\\right) \\\\right) = \\\\frac{1}{\\\\sqrt{a^2-(f(y))^2}} \\\\cdot \\\\frac{\\\\partial}{\\\\partial y} \\\\left( f(y) \\\\right)$. i.e. $\\\\frac{1}{\\\\sqrt{(\\\\text{bottom})^2-(\\\\text{top})^2}} \\\\times \\\\left( \\\\text{derivative of the top} \\\\right)$\"],\n [\"1/sqrt(y^2-x^2)\", \"There are two things to note here. Firstly, you are looking for the partial derivative with respect to $y$ here. Remember that, in the rule given on page 25 of the log tables for differentiating $\\\\sin^{-1} \\\\left( \\\\frac{x}{a} \\\\right)$, the $x$ is something to do with the variable, while $a$ is a number. Can you rewrite $\\\\sin^{-1} \\\\left( \\\\frac{x}{y} \\\\right)$ so that it looks like $\\\\sin^{-1} \\\\left( \\\\frac{\\\\text{something to do with } y}{\\\\text{a number}} \\\\right)$? Secondly, once you have written $\\\\sin^{-1} \\\\left( \\\\frac{x}{y} \\\\right)$ in this way, don't forget to multiply by the derivative of the top, i.e. the derivative will be $\\\\frac{1}{\\\\sqrt{(\\\\text{bottom})^2-(\\\\text{top})^2}} \\\\times \\\\left( \\\\text{derivative of the top} \\\\right)$.\"],\n [\"-1/sqrt(y^2-x^2)*x/y^2\", \"You are looking for the partial derivative with respect to $y$ here. Remember that, in the rule given on page 25 of the log tables for differentiating $\\\\sin^{-1} \\\\left( \\\\frac{x}{a} \\\\right)$, the $x$ is something to do with the variable, while $a$ is a number. Can you rewrite $\\\\sin^{-1} \\\\left( \\\\frac{x}{y} \\\\right)$ so that it looks like $\\\\sin^{-1} \\\\left( \\\\frac{\\\\text{something to do with } y}{\\\\text{a number}} \\\\right)$?\"]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x),\"feedback\":x],\n x,\n malrules\n )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n map(\n len(filter(not x ,x,map(\n try(\n resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n message,\n false\n ),\n vars,\n vset\n )))If $z=\\sin^{-1} \\frac{x}{y}$, find $\\frac{\\partial z}{\\partial x}$ and $\\frac{\\partial z}{\\partial y}$.

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