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{"name": "Luis's copy of Differentiate product of trig function and binomial", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "<p>Differentiate the following function $f(x)$ using the product rule.</p>", "tags": ["Calculus", "checked2015", "differentiating a product", "differentiating trigonometric functions", "differentiation", "MAS1601", "product rule", "Steps", "trigonometric functions"], "functions": {}, "question_groups": [{"name": "", "pickQuestions": 0, "pickingStrategy": "all-ordered", "questions": []}], "variables": {"m": {"group": "Ungrouped variables", "definition": "random(2..8)", "templateType": "anything", "description": "", "name": "m"}, "b": {"group": "Ungrouped variables", "definition": "s1*random(1..5)", "templateType": "anything", "description": "", "name": "b"}, "a": {"group": "Ungrouped variables", "definition": "random(1..4)", "templateType": "anything", "description": "", "name": "a"}, "s1": {"group": "Ungrouped variables", "definition": "random(1,-1)", "templateType": "anything", "description": "", "name": "s1"}, "n": {"group": "Ungrouped variables", "definition": "random(2..6)", "templateType": "anything", "description": "", "name": "n"}}, "name": "Luis's copy of Differentiate product of trig function and binomial", "ungrouped_variables": ["a", "s1", "b", "m", "n"], "variable_groups": [], "type": "question", "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "<p>Differentiate $ (a+bx) ^ {m} \\sin(nx)$</p>", "notes": "\n\t\t<p><strong>31/07/2012:</strong></p>\n\t\t<p>Added tags.</p>\n\t\t<p>Added description.</p>\n\t\t<p>Steps problem to be addressed. Now resolved.</p>\n\t\t<p>Checked calculation.OK.</p>\n\t\t<p>Improved prompt display.</p>\n\t\t<p>Clicking on Show steps not lose any marks.</p>\n\t\t", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "parts": [{"stepsPenalty": 0, "prompt": "\n\t\t\t<p>$\\simplify[std]{f(x) = ({a} + {b} * x) ^ {m} * sin({n} * x)}$</p>\n\t\t\t        <p>$\\displaystyle \\frac{df}{dx}=\\;$[[0]]</p>\n\t\t\t        <p>Clicking on Show steps gives you more information, you will not lose any marks by doing so.</p>\n\t\t\t", "steps": [{"type": "information", "prompt": "<p>The product rule says that if $u$ and $v$ are functions of $x$ then<br/>\\[\\simplify[std]{Diff(u * v,x,1) = u * Diff(v,x,1) + v * Diff(u,x,1)}\\]</p>", "scripts": {}, "showCorrectAnswer": true, "marks": 0}], "gaps": [{"checkvariablenames": false, "vsetrangepoints": 5, "expectedvariablenames": [], "marks": 3, "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrange": [0, 1], "scripts": {}, "answersimplification": "std", "answer": "{m*b}({a} + {b} * x) ^ {m-1} * sin({n} * x)+{n}*({a} + {b} * x) ^ {m} * cos({n} * x)", "showCorrectAnswer": true, "checkingtype": "absdiff"}], "scripts": {}, "type": "gapfill", "showCorrectAnswer": true, "marks": 0}], "rulesets": {"surdf": [{"pattern": "a/sqrt(b)", "result": "(sqrt(b)*a)/b"}], "std": ["all", "!collectNumbers", "fractionNumbers"]}, "advice": "\n\t    \n\t    \n\t    <p>The product rule says that if $u$ and $v$ are functions of $x$ then<br/>\\[\\simplify[std]{Diff(u * v,x,1) = u * Diff(v,x,1) + v * Diff(u,x,1)}\\]</p>\n\t    \n\t    \n\t    \n\t    <p>For this example:</p>\n\t    \n\t    \n\t    \n\t    <p>\\[\\simplify[std]{u = ({a} + {b} * x) ^ {m}}\\Rightarrow \\simplify[std]{Diff(u,x,1) = {m * b} * ({a} + {b} * x) ^ {m -1}}\\]</p>\n\t    \n\t    \n\t    \n\t    <p>\\[\\simplify[std]{v = sin({n} * x)} \\Rightarrow \\simplify[std]{Diff(v,x,1) = {n} * cos({n} * x)}\\]</p>\n\t    \n\t    \n\t    \n\t    <p>Hence on substituting into the product rule above we get:</p>\n\t    \n\t    \n\t    \n\t    <p>\\[\\simplify[std]{Diff(f,x,1) = {m*b}({a} + {b} * x) ^ {m-1} * sin({n} * x)+{n}*({a} + {b} * x) ^ {m} * cos({n} * x)}\\]</p>\n\t    \n\t    \n\t", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}