// Numbas version: exam_results_page_options
{"name": "Numbastest uke 39: Derivasjon", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], []], "questions": [{"name": "Gjennomsnittlige VF", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>En funksjon $f$ er gitt ved $f(x)=\\simplify{x^2+{b}*x+{c}}$.&nbsp;</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/j7qmetrb',defs)}</p>", "advice": "<p>Den gjennomsnittlige vekstfarten for $f$ n&aring;r $x$ vokser fra $x=\\var{x1}$ til $x=\\var{x2}$ blir</p>\n<p>$\\dfrac{\\Delta y}{\\Delta x}=\\dfrac{f(\\var{x2}-f(\\var{x1})}{\\var{x2}-\\var{x1}}=\\dfrac{(\\var{x2}^2+\\var{b}\\cdot\\var{x2}+\\var{c})-(\\var{x1}^2+\\var{b}\\cdot\\var{x1}+\\var{c})}{\\var{x2-x1}}=\\dfrac{\\var{x2^2+b*x2+c}-\\var{x1^2+b*x1+c}}{\\var{x2-x1}}=\\dfrac{\\var{x2^2+b*x2+c-x1^2+b*x1+c}}{\\var{x2-x1}}=\\var{(x2^2+b*x2+c-x1^2+b*x1+c)/(x2-x1)}$</p>", "rulesets": {}, "variables": {"b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(2..3)", "description": "", "templateType": "anything"}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(4..6)", "description": "", "templateType": "anything"}, "defs": {"name": "defs", "group": "Ungrouped variables", "definition": "[['b',b],['c',c],['x1',x1],['x2',x2]]", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["b", "c", "x1", "x2", "defs"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn den gjennomsnittlige vekstfarten til $f$ n&aring;r $x$ vokser fra $x=\\var{x1}$ til $x=\\var{x2}$</p>\n<p>$\\dfrac{\\Delta y}{\\Delta x}=$</p>", "answer": "{((x2^2+b*x2+c)-(x1^2+b*x1+c))/(x2-x1)}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Linearisering", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>M&aring;let i denne oppgaven er &aring; finne god tiln&aelig;rming til $\\sqrt{\\var{k^2+1}}$.</p>\n<p>La oss sette en funksjon $f(x)=\\sqrt{x}$</p>", "advice": "<p>Linearisering til $f(x)$ i punkt $x=x_0+\\Delta x$ er gitt ved</p>\n<p>$F(x)\\approx f'(x_0)(x-x_0)+f(x_0)$.</p>\n<p>Da linearisering til $f(x)=\\sqrt{x}$ i punkt $\\var{k^2+1}$ er gitt ved</p>\n<p>$F(\\var{k^2+1})\\approx f'(\\var{k^2})(\\var{k^2+1}-\\var{k^2})+f(\\var{k^2})=\\frac{1}{2\\cdot\\var{k}}\\cdot 1+\\var{k}=\\simplify{{k+1/(2*k)}}$.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"k": {"name": "k", "group": "Ungrouped variables", "definition": "random(3..6)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["k"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>F&oslash;rst, skriv inn det n&aelig;rmeste tallet til $\\var{k^2+1}$ som du kan finne kvadratrota av uten kalkulator (der kvadratrota blir et heltall)</p>\n<p>$x_0=$[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{k^2}", "maxValue": "{k^2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn den deriverte til $f(x)$ (Bruk sqrt(x) for &aring; skrive $\\sqrt{x}$)</p>", "answer": "1/(2*sqrt(x))", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn $f'(x_0)$, hvor $x_0$ er tallet du fant i a).</p>", "minValue": "1/(2*k)", "maxValue": "1/(2*k)", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Lineariseringen til $f(x)$ i punkt $x=x_0$, hvor $x_0$ er tallet du fant i a), blir</p>\n<p>$F(x)=f'($[[1]]$)\\cdot(x-$[[2]] $)+f($[[3]] $)\\,\\,\\,=\\,\\,\\,$[[0]]$\\cdot(x-$[[5]]$)+$[[4]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "1/(2*k)", "maxValue": "1/(2*k)", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{k^2}", "maxValue": "{k^2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{k^2}", "maxValue": "{k^2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "k^2", "maxValue": "k^2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "k", "maxValue": "k", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "k^2", "maxValue": "k^2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn $F(\\var{k^2+1})$. (Husk: Bruk punktum, ikke komma for &aring; skrive desimaltall)</p>", "minValue": "1/{2*k}+{k}", "maxValue": "1/{2*k}+{k}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Bruk kalkulator for &aring; finne $\\sqrt{\\var{k^2+1}}$</p>", "minValue": "{sqrt(k^2+1)}", "maxValue": "{sqrt(k^2+1)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Sammenlikn resultatene i oppgavene e) og f)</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Tangentlinja til grafen", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>La funksjonen $f$ v&aelig;re gitt ved $f(x)=\\simplify{{a}x^2+{b}x+{c}}$.&nbsp;</p>", "advice": "<p>Likningen til tangenten til $f(x)$ i punkt $x=c$ er</p>\n<p>$y=f'(c)(x-c)+f(c)$</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-3..3 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-3..3 except a)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-10..10 except 0)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn den deriverte $f'(x)$</p>", "answer": "2*{a}*x+{b}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Finn den deriverte i punktet $x=\\var{d}$, dvs. $f'(\\var{d})$</p>", "minValue": "{2*a*d+b}", "maxValue": "{2*a*d+b}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Likningen til tangenten til $f(x)$ i punktet $x=\\var{d}$ blir $y=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{2*a*d+b}*(x-{d})+{a*d^2+b*d+c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Definisjon av den deriverte", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>En funksjon $f$ er gitt ved $f(x)=\\simplify{{a}*x^2+{b}x+{c}}$</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-2..2 except 0)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-3..3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Regn f&oslash;rst ut den deriverte til $f(x)$, $f'(x)=$[[4]]</p>\n<p>Bruk n&aring; definisjonen til den deriverte for &aring; finne $f'(x)$</p>\n<p>(Merk: N&aring;r du trenger &aring; skrive inn $xh$ bruk * mellom: x*h)</p>\n<p>Den deriverte til funksjonen $f(x)$ er definert ved</p>\n<p>$f'(x)=\\lim\\limits_{h\\rightarrow0}\\dfrac{f(x+h)-f(x)}{h}$</p>\n<p></p>\n<p>F&oslash;rst finn $f(x+h)=$[[0]]</p>\n<p></p>\n<p>videre regn ut $f(x+h)-f(x)=$[[1]]</p>\n<p></p>\n<p>Forenkle $\\dfrac{f(x+h)-f(x)}{h}$=[[2]]</p>\n<p></p>\n<p>Da $f'(x)=\\lim\\limits_{h\\rightarrow0}\\dfrac{f(x+h)-f(x)}{h}=$[[3]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a}*(x+h)^2+{b}*(x+h)+{c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "h", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a}*(2*x*h+h^2)+{b}*h", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "h", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a}*(2*x+h)+{b}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "h", "value": ""}, {"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "2*{a}*x+{b}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "2*{a}*x+{b}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Derivasjon med hensyn p\u00e5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Infinitesimal-notasjonen hjelper oss til &aring; markere hvilken variabel vi deriverer med hensyn p&aring; n&aring;r vi har utrykk med flere bokstaver/symboler og det ikke er gitt hvilke av bokstavene/symbolene som er gjeldende variabel.</p>\n<p><strong>Deriver funksjonene under.</strong></p>\n<p>Hint: For &aring; skrive inn f.eks. $\\frac{1}{x^3}$ b&oslash;r man skrive 1/(x^3), for &aring; skrive inn $\\cos^2x$ b&oslash;r man skrive (cos(x))^2, og n&aring;r du trenger &aring; skrive inn produktet av to \"bokstaver\" $xh$ bruk * mellom: x*h</p>", "advice": "<p>Uttrykket $\\dfrac{d f}{d\\var{inp2}}$ leses som \"$f$ derivert med hensyn p&aring; $\\var{inp2}$\". N&aring;r $\\dfrac{d}{d\\var{inp2}}$ st&aring;r foran noe, er meningen at uttrykket bak skal deriveres med $\\var{inp2}$ som variabel.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"inp1": {"name": "inp1", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out1": {"name": "out1", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "k1": {"name": "k1", "group": "Ungrouped variables", "definition": "random(5..9 except 1)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3..33)", "description": "", "templateType": "anything", "can_override": false}, "k2": {"name": "k2", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k3": {"name": "k3", "group": "Ungrouped variables", "definition": "random(5..8)", "description": "", "templateType": "anything", "can_override": false}, "k4": {"name": "k4", "group": "Ungrouped variables", "definition": "random(3..11 except k1)", "description": "", "templateType": "anything", "can_override": false}, "k5": {"name": "k5", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k6": {"name": "k6", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k7": {"name": "k7", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k8": {"name": "k8", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "inp2": {"name": "inp2", "group": "Ungrouped variables", "definition": "expression(random('r','s','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp3": {"name": "inp3", "group": "Ungrouped variables", "definition": "expression(random('x','t'))", "description": "", "templateType": "anything", "can_override": false}, "inp4": {"name": "inp4", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp5": {"name": "inp5", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp6": {"name": "inp6", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp7": {"name": "inp7", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp8": {"name": "inp8", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out2": {"name": "out2", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out3": {"name": "out3", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out4": {"name": "out4", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out5": {"name": "out5", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out6": {"name": "out6", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out7": {"name": "out7", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out8": {"name": "out8", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["inp1", "out1", "k1", "a", "k2", "k3", "k4", "k5", "k6", "k7", "k8", "inp2", "inp3", "inp4", "inp5", "inp6", "inp7", "inp8", "out2", "out3", "out4", "out5", "out6", "out7", "out8"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\dfrac{d}{d\\var{inp1}}(\\simplify{{inp1}^{k1}+{k2}})=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k1}*{inp1}^({k1-1})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\dfrac{d}{d\\var{inp3}}(\\simplify{{inp2} {inp3}^{k3}+{inp3}^{k4}})=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{inp2}*{k3}*{inp3}^({k3-1})+{k4}*{inp3}^({k4-1})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\dfrac{d}{d\\var{inp2}}(\\simplify{{inp2} {inp3}^{k3}+{inp3}^{k4}})=$[[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{inp3}^({k3})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Spesielle derivasjonsregler", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p><strong>Deriver funksjonene under.</strong></p>\n<p>Hint: For &aring; skrive inn f.eks. $\\frac{1}{x^{3a}}$ b&oslash;r man skrive 1/(x^(3a)), for &aring; skrive inn $\\cos^2x$ b&oslash;r man skrive (cos(x))^2</p>", "advice": "<p>Bruk f&oslash;lgende spesielle derivasjonsregler</p>\n<p>$f(x)=a$ gir $f'(x)=0$ ($a$ er et konstant)</p>\n<p>$f(x)=ax$ gir $f'(x)=a$ ($a$ er et konstant)</p>\n<p>$f(x)=x^a$ gir $f'(x)=ax^{a-1}$ ($a\\neq0$ er et konstant)</p>\n<p>$f(x)=\\sin(kx)$ gir $f'(x)=k\\cos(kx)$ ($k$ er et konstant, $x$ er i radianer)</p>\n<p>$f(x)=\\cos(kx)$ gir $f'(x)=-k\\sin(kx)$ ($k$ er et konstant, $x$ er i radianer)</p>\n<p>$f(x)=\\tan(kx)$ gir $f'(x)=k\\dfrac{1}{\\cos^2(kx)}$ ($k$ er et konstant, $x$ er i radianer)</p>\n<p>$f(x)=e^{kx}$ gir $f'(x)=ke^{kx}$ ($k$ er et konstant)</p>\n<p>$f(x)=\\ln(kx)$ gir $f'(x)=\\frac{1}{x}$ ($k$ er et konstant)</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"inp1": {"name": "inp1", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out1": {"name": "out1", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "k1": {"name": "k1", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "random(3..33)", "description": "", "templateType": "anything", "can_override": false}, "k2": {"name": "k2", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k3": {"name": "k3", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k4": {"name": "k4", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k5": {"name": "k5", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k6": {"name": "k6", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k7": {"name": "k7", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "k8": {"name": "k8", "group": "Ungrouped variables", "definition": "random(-56..56 except 0 except -1 except 1)", "description": "", "templateType": "anything", "can_override": false}, "inp2": {"name": "inp2", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp3": {"name": "inp3", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp4": {"name": "inp4", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp5": {"name": "inp5", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp6": {"name": "inp6", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp7": {"name": "inp7", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "inp8": {"name": "inp8", "group": "Ungrouped variables", "definition": "expression(random('x','r','s','t','w'))", "description": "", "templateType": "anything", "can_override": false}, "out2": {"name": "out2", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out3": {"name": "out3", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out4": {"name": "out4", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out5": {"name": "out5", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out6": {"name": "out6", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out7": {"name": "out7", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}, "out8": {"name": "out8", "group": "Ungrouped variables", "definition": "expression(random('f','h','g','p','q','y'))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["inp1", "out1", "k1", "a", "k2", "k3", "k4", "k5", "k6", "k7", "k8", "inp2", "inp3", "inp4", "inp5", "inp6", "inp7", "inp8", "out2", "out3", "out4", "out5", "out6", "out7", "out8"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out1}}(\\simplify{{inp1}})=\\var{inp1}^\\var{k1}$</p>\n<p>$\\simplify{{out1}}'(\\simplify{{inp1}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k1}*{inp1}^({k1-1})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out2}}(\\simplify{{inp2}})=\\var{k2}$</p>\n<p>$\\simplify{{out2}}'(\\simplify{{inp2}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "0", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out3}}(\\simplify{{inp3}})=\\sin(\\var{k3}\\var{inp3})$</p>\n<p>$\\simplify{{out3}}'(\\simplify{{inp3}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k3}*cos({k3}*{inp3})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out4}}(\\simplify{{inp4}})=\\cos(\\var{k4}\\var{inp4})$</p>\n<p>$\\simplify{{out4}}'(\\simplify{{inp4}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "-{k4}*sin({k4}*{inp4})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out5}}(\\simplify{{inp5}})=\\tan(\\var{k5}\\var{inp5})$</p>\n<p>$\\simplify{{out5}}'(\\simplify{{inp5}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k5}/(cos({k5}*{inp5}))^2", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out6}}(\\simplify{{inp6}})=e^{\\var{k6}\\var{inp6}}$</p>\n<p>$\\simplify{{out6}}'(\\simplify{{inp6}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k6}*e^({k6}*{inp6})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out7}}(\\simplify{{inp7}})=\\ln({\\var{k7}\\var{inp7}})$</p>\n<p>$\\simplify{{out7}}'(\\simplify{{inp7}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "1/{inp7}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out8}}(\\simplify{{inp8}})=\\var{a}^{{\\var{k8}\\var{inp8}}}$</p>\n<p>$\\simplify{{out8}}'(\\simplify{{inp8}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{k8}*{a}^({k8}*{inp8})*ln({a})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "extensions": ["geogebra"], "custom_part_types": [], "resources": []}