// Numbas version: exam_results_page_options
{"name": "Generelle derivasjonsregler", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Generelle derivasjonsregler", "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p><strong>Deriver funksjonene under.</strong></p>\n<p>Merk: 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. Bruk * n&aring;r det skal v&aelig;re et produkt mellom to bokstaver.</p>", "advice": "<p>Bruk f&oslash;lgende generelle derivasjonsregler</p>\n<p>$f(x)=a\\cdot u(x)$ gir $f'(x)=a\\cdot u'(x)$ ($a$ er et konstant)</p>\n<p>$f(x)=u(x)+v(x)$ gir $f'(x)=u'(x)+v'(x)$&nbsp;</p>\n<p>$f(x)=u(x)-v(x)$ gir $f'(x)=u'(x)-v'(x)$&nbsp;</p>\n<p>$f(x)=u(x)\\cdot v(x)$ gir $f'(x)=u'(x)\\cdot v(x)+u(x)\\cdot v'(x)$&nbsp; (produktregelen)</p>\n<p>$f(x)=\\dfrac{u(x)}{v(x)}$ gir $f'(x)=\\dfrac{u'(x)\\cdot v(x)-u(x)\\cdot v'(x)}{v^2(x)}$ (br&oslash;kregelen)</p>\n<p>$f(x)=g(u(x))$ gir $f'(x)=g'(u(x))\\cdot u'(x)$ (kjerneregelen)</p>", "rulesets": {}, "extensions": [], "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", 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"variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out1}}(\\simplify{{inp1}})=\\simplify{{k1}*sin({inp1})-{k2-1}*{inp1}^{{a}}+1/{inp1}}$</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}*cos({inp1})-{a*(k2-1)}*{inp1}^({a-1})-1/({inp1}^2)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, 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"<p>$\\simplify{{out3}}(\\simplify{{inp3}})=\\var{k3}^\\var{inp3}\\cos(\\var{inp3})$</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}^{inp3}*ln({k3})*cos({inp3})-{k3}^{inp3}*sin({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>$\\simplify{{out4}}(\\simplify{{inp4}})=\\dfrac{\\cos(\\var{inp4})}{\\sin(\\var{inp4})}$</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": "(-(cos({inp4}))^2-(sin({inp4}))^2)/((sin({inp4}))^2)", 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"extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out6}}(\\simplify{{inp6}})=(\\simplify{{inp6}^{{k6}}+{inp6}+{k7}})(\\simplify{{inp6}^{{k7-2}}+{inp6}})$</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}*{inp6}^({k6}-1)+1)*({inp6}^({k7}-2)+{inp6})+({inp6}^({k6})+{inp6}+{k7})*(({k7}-2)*{inp6}^({k7}-3)+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>$\\simplify{{out7}}(\\simplify{{inp7}})=(\\var{k2}+\\var{inp7}^{\\var{k4}})^{\\var{k6}}$</p>\n<p>$\\simplify{{out7}}'(\\simplify{{inp7}})=$ [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, 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"variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify{{out8}}(\\simplify{{inp8}})=\\cos(\\simplify{{inp8}^{{k8}}+{inp8}+{k1}})$</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": "-sin({inp8}^({k8})+{inp8}+{k1})*({k8}*{inp8}^({k8}-1)+1)", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, 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