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{"name": "CF Maths In class test two mock paper question 5 (iii)", "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"], "name": "CF Maths In class test two mock paper question 5 (iii)", "tags": [], "advice": "<p>With these questions, the chain rule is carried out twice.</p>\n<p>They are essentially the same as the questions in&nbsp;<em>'Differentiation 6 - Exponentials'</em>, but instead of being, say, $e^{2x}$, they are something more like $e^{x^2}$.</p>\n<p>Exactly the same method is carried out.</p>\n<p>Firstly, differentiate the power of $e$. In this case, we differentiate $x^2$ to get $2x$.</p>\n<p>Now times this result by the coefficient (the coefficient here being $1$), to get a final result of:</p>\n<p style=\"text-align: center;\">$2xe^{x^2}$</p>", "rulesets": {}, "parts": [{"prompt": "<p>$y=\\var{c[1]}e^{\\var{c[0]}x+\\var{c[2]}}$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["e", "x"], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({c[1]}*{c[0]}x)*e^(x+{c[2]})", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p><strong>Differentiate the following.</strong></p>\n<p>You will need to use the chain rule within these questions.</p>\n<p>Do not write out $dy/dx$; only input the differentiated right hand side of each equation.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"p": {"definition": "repeat(random(1..3),2)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "c": {"definition": "repeat(random(2..8),5)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}}, "metadata": {"notes": "", "description": "<p>Differentiating further exponentials</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}]}], "contributors": [{"name": "Jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/514/"}]}