// Numbas version: finer_feedback_settings
{"name": "Harry's copy of Differentiation: Product rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"question_groups": [{"pickQuestions": 0, "name": "", "pickingStrategy": "all-ordered", "questions": []}], "variablesTest": {"maxRuns": 100, "condition": ""}, "name": "Harry's copy of Differentiation: Product rule", "parts": [{"type": "gapfill", "stepsPenalty": 0, "marks": 0, "prompt": "\n\t\t\t<p>$\\simplify[std]{f(x) = x ^ {m} * cos({a} * x+{b})}$</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", "gaps": [{"showpreview": true, "expectedvariablenames": [], "answersimplification": "std", "checkingaccuracy": 0.001, "vsetrangepoints": 5, "showCorrectAnswer": true, "type": "jme", "marks": 3, "checkingtype": "absdiff", "answer": "{m}x ^ {m-1} * cos({a} * x+{b})-{a}x^{m} * sin({a} * x+{b})", "vsetrange": [0, 1], "checkvariablenames": false, "scripts": {}}], "steps": [{"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>", "type": "information", "showCorrectAnswer": true, "marks": 0, "scripts": {}}], "showCorrectAnswer": true, "scripts": {}}], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"], "surdf": [{"result": "(sqrt(b)*a)/b", "pattern": "a/sqrt(b)"}]}, "tags": ["calculus", "Calculus", "checked2015", "derivative of a product", "differentiating a product", "differentiating trigonometric functions", "differentiation", "MAS1601", "mas1601", "product rule", "Steps", "steps", "trigonometric functions"], "ungrouped_variables": ["a", "s1", "b", "m"], "variable_groups": [], "statement": "<p>Differentiate the following function $f(x)$ using the product rule.</p>", "functions": {}, "type": "question", "showQuestionGroupNames": false, "metadata": {"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 does not lose any marks.</p>\n\t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Differentiate $x^m\\cos(ax+b)$</p>"}, "variables": {"s1": {"group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s1", "templateType": "anything", "description": ""}, "b": {"group": "Ungrouped variables", "definition": "s1*random(1..9)", "name": "b", "templateType": "anything", "description": ""}, "m": {"group": "Ungrouped variables", "definition": "random(2..9)", "name": "m", "templateType": "anything", "description": ""}, "a": {"group": "Ungrouped variables", "definition": "random(2..9)", "name": "a", "templateType": "anything", "description": ""}}, "preamble": {"js": "", "css": ""}, "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 = x ^ {m}}\\Rightarrow \\simplify[std]{Diff(u,x,1) = {m}x ^ {m -1}}\\]</p>\n\t    \n\t    \n\t    \n\t    <p>\\[\\simplify[std]{v = cos({a} * x+{b})} \\Rightarrow \\simplify[std]{Diff(v,x,1) = -{a} * sin({a} * x+{b})}\\]</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}x ^ {m-1} * cos({a} * x+{b})-{a}x^{m} * sin({a} * x+{b})}\\]</p>\n\t    \n\t    \n\t", "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}]}], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}