// Numbas version: exam_results_page_options
{"name": "Differentiation 4 Rule for exponential and natural log", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["num", "ans1", "ans2", "ans3", "num2", "num1"], "parts": [{"marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"vsetrangepoints": 5, "checkingtype": "absdiff", "answer": "{ans1}e^({ans1}x)", "type": "jme", "scripts": {}, "checkingaccuracy": 0.001, "checkvariablenames": false, "marks": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": false, "vsetrange": [0, 1], "showpreview": true, "expectedvariablenames": []}], "type": "gapfill", "scripts": {}, "prompt": "<p>$y = e^{\\var{num[0]}x}$</p>\n<p>$\\frac{dy}{dx} =$&nbsp;[[0]]&nbsp;</p>\n<p></p>"}, {"marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"vsetrangepoints": 5, "checkingtype": "absdiff", "answer": "{ans2}e^({ans2}x)", "type": "jme", "scripts": {}, "checkingaccuracy": 0.001, "checkvariablenames": false, "marks": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrange": [0, 1], "showpreview": true, "expectedvariablenames": []}], "type": "gapfill", "scripts": {}, "prompt": "<p>$y = e^{\\var{num1}x}$</p>\n<p>$\\frac{dy}{dx} =$&nbsp;[[0]]&nbsp;</p>"}, {"marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"vsetrangepoints": 5, "checkingtype": "absdiff", "answer": "{ans3}e^({num2}x)", "type": "jme", "scripts": {}, "checkingaccuracy": 0.001, "checkvariablenames": false, "marks": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrange": [0, 1], "showpreview": true, "expectedvariablenames": []}], "type": "gapfill", "scripts": {}, "prompt": "<p>$y = \\var{num[1]}e^{\\var{num2}x}$</p>\n<p>$\\frac{dy}{dx} =$&nbsp;[[0]]&nbsp;</p>"}, {"marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"vsetrangepoints": 5, "checkingtype": "absdiff", "answer": "1/x", "type": "jme", "scripts": {}, "checkingaccuracy": 0.001, "checkvariablenames": false, "marks": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrange": [0, 1], "showpreview": true, "expectedvariablenames": []}], "type": "gapfill", "scripts": {}, "prompt": "<p>$y = \\ln \\var{num[2]}x$</p>\n<p>$\\frac{dy}{dx} =$&nbsp;[[0]]&nbsp;</p>"}, {"marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"vsetrangepoints": 5, "checkingtype": "absdiff", "answer": "1/x", "type": "jme", "scripts": {}, "checkingaccuracy": 0.001, "checkvariablenames": false, "marks": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrange": [0, 1], "showpreview": true, "expectedvariablenames": []}], "type": "gapfill", "scripts": {}, "prompt": "<p>$y = \\ln \\var{num[3]}x$</p>\n<p>$\\frac{dy}{dx} =$&nbsp;[[0]]&nbsp;</p>"}, {"marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "gaps": [{"vsetrangepoints": 5, "checkingtype": "absdiff", "answer": "1/x", "type": "jme", "scripts": {}, "checkingaccuracy": 0.001, "checkvariablenames": false, "marks": 1, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "vsetrange": [0, 1], "showpreview": true, "expectedvariablenames": []}], "type": "gapfill", "scripts": {}, "prompt": "<p>$y = \\ln \\var{num[4]}x$</p>\n<p>$\\frac{dy}{dx} =$&nbsp;[[0]]&nbsp;</p>"}], "extensions": [], "name": "Differentiation 4 Rule for exponential and natural log", "variables": {"num2": {"definition": "random(-5..-2)", "templateType": "anything", "name": "num2", "group": "Ungrouped variables", "description": ""}, "num": {"definition": "shuffle(2..8)[0..5]", "templateType": "anything", "name": "num", "group": "Ungrouped variables", "description": ""}, "num1": {"definition": "random(0.5..4.5)", "templateType": "anything", "name": "num1", "group": "Ungrouped variables", "description": ""}, "ans1": {"definition": "num[0]", "templateType": "anything", "name": "ans1", "group": "Ungrouped variables", "description": ""}, "ans3": {"definition": "num2*num[1]", "templateType": "anything", "name": "ans3", "group": "Ungrouped variables", "description": ""}, "ans2": {"definition": "num1", "templateType": "anything", "name": "ans2", "group": "Ungrouped variables", "description": ""}}, "preamble": {"css": "", "js": ""}, "variable_groups": [], "metadata": {"licence": "None specified", "description": ""}, "rulesets": {}, "statement": "<p>Remember the rules:</p>\n<p>$y = e^&nbsp;x &nbsp;=&gt; \\frac{dy}{dx} = e^&nbsp;x$</p>\n<p>$y = e^ {ax} &nbsp;=&gt; \\frac{dy}{dx} = ae^ {ax}$</p>\n<p>$y = \\ln (x) &nbsp;=&gt; \\frac{dy}{dx} = \\frac{1}{x}$</p>\n<p>$y = \\ln (ax) &nbsp;=&gt; \\frac{dy}{dx} = \\frac{1}{x}$</p>\n<p>Differentiate each of the following:</p>", "functions": {}, "advice": "<p>i)&nbsp;</p>\n<p>$y = e^{\\var{num[0]}x}$</p>\n<p>$\\frac{dy}{dx} = \\var{ans1}e^{\\var{num[0]}x}$</p>\n<p>ii)&nbsp;</p>\n<p>$y = e^{\\var{num1}x}$</p>\n<p>$\\frac{dy}{dx} =&nbsp;\\var{ans2}e^{\\var{num1}x}$</p>\n<p>iii)&nbsp;</p>\n<p>$y = \\var{num[1]}e^{\\var{num2}x}$</p>\n<p>$\\frac{dy}{dx} = (\\var{num[1]}&nbsp;\\times \\var{num2})e^{\\var{num2}x}&nbsp;=&nbsp;\\var{ans3}e^{\\var{num2}x}$</p>\n<p>iv)&nbsp;</p>\n<p>$y = \\ln \\var{num[2]}x$</p>\n<p>$\\frac{dy}{dx} = \\frac{1}{x}$</p>\n<p>v)&nbsp;</p>\n<p>$y = \\ln \\var{num[3]}x$</p>\n<p>$\\frac{dy}{dx} = \\frac{1}{x}$</p>\n<p>vi)&nbsp;</p>\n<p>$y = \\ln \\var{num[4]}x$</p>\n<p>$\\frac{dy}{dx} = \\frac{1}{x}$</p>", "tags": ["rebelmaths"], "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}