// Numbas version: exam_results_page_options
{"name": "Differentiation 2 General Rule for fractional and negative indices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ans31": {"description": "", "definition": "p3*num[0]", "group": "Ungrouped variables", "templateType": "anything", "name": "ans31"}, "ans51": {"description": "", "definition": "n51*n52*-1", "group": "Ungrouped variables", "templateType": "anything", "name": "ans51"}, "p2": {"description": "", "definition": "shuffle(3..7 except 6)[0..2]", "group": "Ungrouped variables", "templateType": "anything", "name": "p2"}, "ans11": {"description": "", "definition": "1/p1", "group": "Ungrouped variables", "templateType": "anything", "name": "ans11"}, "num": {"description": "", "definition": "shuffle(2..5)[0..2]", "group": "Ungrouped variables", "templateType": "anything", "name": "num"}, "n51": {"description": "", "definition": "random(3..6)", "group": "Ungrouped variables", "templateType": "anything", "name": "n51"}, "ans22": {"description": "", "definition": "ans21-1", "group": "Ungrouped variables", "templateType": "anything", "name": "ans22"}, "n52": {"description": "", "definition": "random(3..6 except n51)", "group": "Ungrouped variables", "templateType": "anything", "name": "n52"}, "p3": {"description": "", "definition": "random(-6..-2)", "group": "Ungrouped variables", "templateType": "anything", "name": "p3"}, "p1": {"description": "", "definition": "random(2..4)", "group": "Ungrouped variables", "templateType": "anything", "name": "p1"}, "ans52": {"description": "", "definition": "(n52*-1)-1", "group": "Ungrouped variables", "templateType": "anything", "name": "ans52"}, "ans41": {"description": "", "definition": "0.5*num[1]", "group": "Ungrouped variables", "templateType": "anything", "name": "ans41"}, "ans42": {"description": "", "definition": "-0.5", "group": "Ungrouped variables", "templateType": "anything", "name": "ans42"}, "ans61": {"description": "", "definition": "n6/2", "group": "Ungrouped variables", "templateType": "anything", "name": "ans61"}, "ans62": {"description": "", "definition": "ans61-1", "group": "Ungrouped variables", "templateType": "anything", "name": "ans62"}, "ans21": {"description": "", "definition": "p2[0]/p2[1]", "group": "Ungrouped variables", "templateType": "anything", "name": "ans21"}, "ans32": {"description": "", "definition": "p3-1", "group": "Ungrouped variables", "templateType": "anything", "name": "ans32"}, "ans12": {"description": "", "definition": "ans11-1", "group": "Ungrouped variables", "templateType": "anything", "name": "ans12"}, "n6": {"description": "", "definition": "random([3,5,7,9])", "group": "Ungrouped variables", "templateType": "anything", "name": "n6"}}, "tags": ["rebelmaths"], "rulesets": {}, "extensions": [], "name": "Differentiation 2 General Rule for fractional and negative indices", "statement": "<p>Remember the rule:</p>\n<p>If $y = ax^n$ then $\\frac{dy}{dx} = anx^{n-1}$</p>\n<p></p>\n<p>Differentiate each of the following:</p>", "variable_groups": [], "preamble": {"js": "", "css": ""}, "functions": {}, "advice": "<p>i)&nbsp;</p>\n<p>$y = x^{\\frac{1}{\\var{p1}}}$</p>\n<p>$\\frac{dy}{dx} = \\var{ans11}x^{(\\frac{1}{\\var{p1}}-1)} = \\var{ans11}x^{\\var{ans12}}$</p>\n<p>ii)&nbsp;</p>\n<p>$y = x^{\\frac{\\var{p2[0]}}{\\var{p2[1]}}}$</p>\n<p>$\\frac{dy}{dx} =&nbsp;\\frac{\\var{p2[0]}}{\\var{p2[1]}}x^{(\\frac{\\var{p2[0]}}{\\var{p2[1]}}-1)} = \\var{ans21}x^{\\var{ans22}}$</p>\n<p>iii)&nbsp;</p>\n<p>$y = \\var{num[0]}x^{\\var{p3}}$</p>\n<p>$\\frac{dy}{dx} = \\var{ans31}x^{(\\var{p3}-1)} = \\var{ans31}x^{\\var{ans32}}$</p>\n<p>iv)&nbsp;</p>\n<p>$y = \\var{num[1]}\\sqrt(x) = \\var{num[1]}x^{\\frac{1}{2}}$</p>\n<p>$\\frac{dy}{dx} = \\frac{\\var{num[1]}}{2}x^{(\\frac{1}{2}-1)} = \\var{ans41}x^{\\var{ans42}}$</p>\n<p>v)&nbsp;</p>\n<p>$y = \\frac{\\var{n51}}{x^{\\var{n52}}} = \\var{n51}x^{-\\var{n52}}$</p>\n<p>$\\frac{dy}{dx} = \\var{ans51}x^{(-\\var{n52}-1)} = \\var{ans51}x^{\\var{ans52}}$</p>\n<p>vi)&nbsp;</p>\n<p>$y = \\sqrt(x^\\var{n6}) = x^{\\frac{\\var{n6}}{2}}$</p>\n<p>$\\frac{dy}{dx} = \\frac{\\var{n6}}{2}x^{(\\frac{\\var{n6}}{2}-1)} = \\var{ans61}x^{\\var{ans62}}$</p>", "ungrouped_variables": ["p2", "num", "ans11", "ans12", "ans21", "ans22", "ans31", "ans32", "p1", "p3", "ans41", "ans42", "ans51", "n51", "n52", "ans52", "n6", "ans61", "ans62"], "parts": [{"customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "prompt": "<p>$y = \\var{num[0]}x^{\\var{p3}}$</p>\n<p>$\\frac{dy}{dx} =$&nbsp;[[0]]&nbsp;</p>", "extendBaseMarkingAlgorithm": true, "unitTests": [], "sortAnswers": false, "type": "gapfill", "marks": 0, "scripts": {}, "adaptiveMarkingPenalty": 0, "customName": "", "variableReplacements": [], "gaps": [{"checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "checkVariableNames": false, "checkingType": "absdiff", "showPreview": true, "type": "jme", "scripts": {}, "adaptiveMarkingPenalty": 0, "customName": "", "vsetRange": [0, 1], "failureRate": 1, "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "x"}], "extendBaseMarkingAlgorithm": true, "answer": "{ans31}x^{ans32}", "unitTests": [], "vsetRangePoints": 5, "marks": 1, "variableReplacements": [], "useCustomName": false, "showCorrectAnswer": true, "showFeedbackIcon": true}], "useCustomName": false, "showCorrectAnswer": true, "showFeedbackIcon": true}, {"customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "prompt": "<p>$y = \\var{num[1]}\\sqrt x$</p>\n<p>$\\frac{dy}{dx} =$&nbsp;[[0]]&nbsp;</p>", "extendBaseMarkingAlgorithm": true, "steps": [{"customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Hint: What is $\\sqrt x$ as a power of $x$</p>", "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "information", "marks": 0, "scripts": {}, "adaptiveMarkingPenalty": 0, "customName": "", "variableReplacements": [], "useCustomName": false, "showCorrectAnswer": true, "showFeedbackIcon": true}], "unitTests": [], "sortAnswers": false, "type": "gapfill", "marks": 0, "scripts": {}, "adaptiveMarkingPenalty": 0, "customName": "", "stepsPenalty": 0, "variableReplacements": [], "gaps": [{"checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "checkVariableNames": false, "checkingType": "absdiff", "showPreview": true, "type": "jme", "scripts": {}, "adaptiveMarkingPenalty": 0, "customName": "", "vsetRange": [0, 1], "failureRate": 1, "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "x"}], "extendBaseMarkingAlgorithm": true, "answer": "{ans41}x^{ans42}", "unitTests": [], "vsetRangePoints": 5, "marks": 1, "variableReplacements": [], "useCustomName": false, "showCorrectAnswer": true, "showFeedbackIcon": true}], "useCustomName": false, "showCorrectAnswer": true, "showFeedbackIcon": true}, {"customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "prompt": "<p>$y = \\frac{\\var{n51}}{x^{\\var{n52}}}$</p>\n<p>$\\frac{dy}{dx} =$&nbsp;[[0]]&nbsp;</p>", "extendBaseMarkingAlgorithm": true, "steps": [{"customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "prompt": "<p>Hint: What is $\\frac{1}{x^2}$ as a power of $x$</p>", "extendBaseMarkingAlgorithm": true, "unitTests": [], "type": "information", "marks": 0, "scripts": {}, "adaptiveMarkingPenalty": 0, "customName": "", "variableReplacements": [], "useCustomName": false, "showCorrectAnswer": true, "showFeedbackIcon": true}], "unitTests": [], "sortAnswers": false, "type": "gapfill", "marks": 0, "scripts": {}, "adaptiveMarkingPenalty": 0, "customName": "", "stepsPenalty": 0, "variableReplacements": [], "gaps": [{"checkingAccuracy": 0.001, "variableReplacementStrategy": "originalfirst", "checkVariableNames": false, "checkingType": "absdiff", "showPreview": true, "type": "jme", "scripts": {}, "adaptiveMarkingPenalty": 0, "customName": "", "vsetRange": [0, 1], "failureRate": 1, "customMarkingAlgorithm": "", "valuegenerators": [{"value": "", "name": "x"}], "extendBaseMarkingAlgorithm": true, "answer": "{ans51}x^{ans52}", "unitTests": [], "vsetRangePoints": 5, "marks": 1, "variableReplacements": [], "useCustomName": false, "showCorrectAnswer": true, "showFeedbackIcon": true}], "useCustomName": false, "showCorrectAnswer": true, "showFeedbackIcon": true}], "metadata": {"description": "", "licence": "None specified"}, "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}]}], "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}