// Numbas version: finer_feedback_settings
{"name": "Harry's copy of Differentiation 8 - Logarithms", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "rulesets": {}, "parts": [{"gaps": [{"checkingaccuracy": 0.001, "marks": 1, "scripts": {}, "showCorrectAnswer": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "type": "jme", "answer": "1/x", "variableReplacements": [], "checkvariablenames": false, "checkingtype": "absdiff", "showpreview": true, "expectedvariablenames": [], "vsetrange": [0, 1], "answersimplification": "all"}], "prompt": "<p>$y=\\ln(x)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>\n<p></p>", "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"gaps": [{"checkingaccuracy": 0.001, "marks": "2", "scripts": {}, "showCorrectAnswer": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "type": "jme", "answer": "-1/x", "variableReplacements": [], "checkvariablenames": false, "checkingtype": "absdiff", "showpreview": true, "expectedvariablenames": [], "vsetrange": [0, 1], "answersimplification": "all"}], "prompt": "<p>$y=-\\ln(\\var{c[0]}x)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"gaps": [{"checkingaccuracy": 0.001, "marks": "2", "scripts": {}, "showCorrectAnswer": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "type": "jme", "answer": "{c[1]}/x", "variableReplacements": [], "checkvariablenames": false, "checkingtype": "absdiff", "showpreview": true, "expectedvariablenames": [], "vsetrange": [0, 1], "answersimplification": "all"}], "prompt": "<p>$y=\\var{c[1]}\\ln(\\var{c[2]}x)$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"gaps": [{"checkingaccuracy": 0.001, "marks": "2", "scripts": {}, "showCorrectAnswer": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "type": "jme", "answer": "{p}x^({p}-1)/(x^{p}+{c[3]})", "variableReplacements": [], "checkvariablenames": false, "checkingtype": "absdiff", "showpreview": true, "expectedvariablenames": [], "vsetrange": [0, 1], "answersimplification": "all"}], "prompt": "<p>$y=\\ln(x^\\var{p}+\\var{c[3]})$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"gaps": [{"checkingaccuracy": 0.001, "marks": "2", "scripts": {}, "showCorrectAnswer": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "type": "jme", "answer": "(2{c[3]}x+{c[4]})/({c[3]}x^2+{c[4]}x+{c[5]})", "variableReplacements": [], "checkvariablenames": false, "checkingtype": "absdiff", "showpreview": true, "expectedvariablenames": [], "vsetrange": [0, 1], "answersimplification": "all"}], "prompt": "<p>$y=\\ln(\\var{c[3]}x^2+\\var{c[4]}x+\\var{c[5]})$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}], "preamble": {"css": "", "js": ""}, "type": "question", "advice": "<p>The differentiate of $\\ln(x)$ is $\\frac{1}{x}$.</p>\n<p>This proof can be found&nbsp;<a href=\"http://www.themathpage.com/acalc/exponential.htm#derivative\">here</a>.</p>\n<p></p>\n<p>For natural logarithms in the form $u\\ln(a(x))$ where $a(x)$ is a function of $x$, the derivative is $u\\frac{a'(x)}{a(x)}$.</p>", "tags": [], "name": "Harry's copy of Differentiation 8 - Logarithms", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Differentiating the natural logarithm</p>"}, "variables": {"p": {"definition": "random(2..5)", "name": "p", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "c": {"definition": "repeat(random(2..7),8)", "name": "c", "group": "Ungrouped variables", "templateType": "anything", "description": ""}}, "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p><strong>Differentiate the following.</strong></p>\n<p>Do not write out $dy/dx$; only input the differentiated right hand side of each equation.</p>", "ungrouped_variables": ["c", "p"], "variable_groups": [], "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/"}]}