// Numbas version: exam_results_page_options
{"name": "QM103_test2_2017_Q6", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "QM103_test2_2017_Q6", "rulesets": {}, "metadata": {"description": "<p>Differentiating the natural logarithm</p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": ["c", "p"], "tags": [], "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>\n<p>Give your answers as you would in Excel</p>\n<p>For example &nbsp;$-\\frac{3}{4}x^2+\\frac{5}{6}x^{-\\frac{4}{5}}-12x+4x^3e^{(2x^2-2)}$</p>\n<p>Would be entered -(3/4)*x^2 &nbsp; +(5/6)*x^(-4/5) &nbsp; -12*x &nbsp; + 4*x^3*e^(2x^2-2)</p>", "extensions": [], "parts": [{"prompt": "<p>$y=\\ln(x^\\var{p}+\\var{c[3]})$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "scripts": {}, "showCorrectAnswer": true, "gaps": [{"answersimplification": "all", "vsetrangepoints": 5, "marks": "2", "scripts": {}, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "answer": "{p}x^({p}-1)/(x^{p}+{c[3]})", "checkingtype": "absdiff", "showpreview": true, "variableReplacements": [], "showCorrectAnswer": true, "vsetrange": [0, 1], "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme"}], "marks": 0, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true}], "variable_groups": [], "preamble": {"js": "", "css": ""}, "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "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>", "variables": {"c": {"name": "c", "description": "", "templateType": "anything", "definition": "repeat(random(2..7),8)", "group": "Ungrouped variables"}, "p": {"name": "p", "description": "", "templateType": "anything", "definition": "random(2..5)", "group": "Ungrouped variables"}}, "type": "question", "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}