// Numbas version: finer_feedback_settings
{"name": "Lois's copy of Bill's copy of Basic Chain Rule", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "a1", "a2"], "name": "Lois's copy of Bill's copy of Basic Chain Rule", "tags": ["Calculus", "calculus", "chain rule", "Differentiation", "differentiation"], "advice": "<p>This&nbsp;<a href=\"http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-table1-2009-1.pdf\">booklet</a> from Mathcentre provides a table of derivatives of common functions.</p>\n<p>From this we see that the derivative of $\\sin mx$ is $m \\cos mx$. In part a $m$ is $\\var{a}$ and we also have $\\var{a1}$ multiplying the whole function. So the derivative is $ (\\var{a} \\times \\var{a1}) \\simplify{cos({a}x+{b})}$.</p>\n<p></p>", "rulesets": {}, "parts": [{"variableReplacements": [], "prompt": "<p>Differentiate with respect to $x$ the function $y = \\simplify{{a1}sin({a}x+{b})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{a}*{a1}cos({a}*x+{b})", "marks": "1", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"variableReplacements": [], "prompt": "<p>Differentiate with respect to $x$ the function $y = \\simplify{{a1}cos({b}x+{a})}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "-{a1}*{b}sin({b}x+{a})", "marks": "1", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "extensions": [], "statement": "<p>Differentiate the functions below.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..10#1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(0.1..1#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-1..1#0.1 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-5..5#0.1 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "a1": {"definition": "random(-10..10#0.5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a2": {"definition": "random(-10..10#0.1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}}, "metadata": {"description": "<p>Using chain rule to differentiate functions of the form asin(mx+b).</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}