// Numbas version: finer_feedback_settings
{"name": "Jinhua's copy of Jinhua's copy of Differentiation 14 - Mixed", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["c", "p", "ex"], "name": "Jinhua's copy of Jinhua's copy of Differentiation 14 - Mixed", "tags": [], "preamble": {"css": "fraction {\n  display: inline-block;\n  vertical-align: middle;\n}\nfraction > numerator, fraction > denominator {\n  float: left;\n  width: 100%;\n  text-align: center;\n  line-height: 2.5em;\n}\nfraction > numerator {\n  border-bottom: 1px solid;\n  padding-bottom: 5px;\n}\nfraction > denominator {\n  padding-top: 5px;\n}\nfraction input {\n    line-height: 1em;\n}\n\nfraction .part {\n    margin: 0;\n}\n\n.table-responsive, .fractiontable {\n  display:inline-block;\n}\n.fractiontable {\n  padding: 0; \n  border: 0;\n}\n\n.fractiontable  .tddenom \n{\n text-align: center;\n}\n\n.fractiontable .tdnum \n{\n  border-bottom: 1px solid black; \n  text-align: center;\n}\n\n\n.fractiontable tr {\n    height: 3em;\n}\n", "js": "document.createElement('fraction');\ndocument.createElement('numerator');\ndocument.createElement('denominator');"}, "advice": "<p>This question takes ideas from all previous parts of the&nbsp;<em>'Differentiation'</em> series. If you struggle, look back at the appropriate sections.</p>", "rulesets": {"std": ["all"]}, "parts": [{"prompt": "<p>$f(x)=\\var{ex[0]}e^x\\sin(\\var{c[0]}x)$</p>\n<p>$f'(x)=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{ex[0]}e^x*(sin({c[0]}x)+{c[0]}cos({c[0]}x))", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$f(x)=\\var{ex[1]}\\sin(\\var{c[1]}x)\\cos(\\var{c[2]}x)$</p>\n<p>$f'(x)=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "{ex[1]}({c[1]}cos({c[1]}x)cos({c[2]}x)-{c[2]}sin({c[1]}x)sin({c[2]}x))", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$f(x)=$&nbsp;&nbsp;<fraction><numerator>$\\ln(\\var{ex[2]}x)$</numerator><denominator>$\\var{c[3]}-\\var{c[4]}x$</denominator></fraction></p>\n<p>$f'(x)=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({c[3]}-{c[4]}x+{c[4]}x*ln({ex[2]}x))/(x*({c[3]}-{c[4]}x)^2)", "marks": "2", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$f(x)=\\var{ex[3]}\\sin(\\ln(x))$</p>\n<p>$f'(x)=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({ex[3]}/x)*cos(ln(x))", "marks": "2", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$f(x)=$&nbsp;&nbsp;<fraction><numerator>$e^{\\var{p}x}$</numerator><denominator>$\\var{c[5]}-x$</denominator></fraction></p>\n<p>$f'(x)=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({p}e^({p}x)({c[5]}-x)+e^({p}x))/({c[5]}-x)^2", "marks": "2", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$f(x)=\\ln(\\var{ex[4]}x)\\sin(\\var{ex[5]}x)$</p>\n<p>$f'(x)=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "(1/x)*sin({ex[5]}x)+{ex[5]}ln({ex[4]}x)*cos({ex[5]}x)", "marks": "2", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p><strong>Find $f'(x)$ of the following, using the appropriate rule.</strong></p>\n<p>Do not write out $f'(x)=$.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"p": {"definition": "random(-4..-2)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "c": {"definition": "repeat(random(2..5),10)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "ex": {"definition": "repeat(random(2..5),6)", "templateType": "anything", "group": "Ungrouped variables", "name": "ex", "description": "<p>extra coeff's added</p>"}}, "metadata": {"notes": "", "description": "<p>Identifying the correct rule to use</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}]}], "contributors": [{"name": "", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}