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{"name": "QM103_test2_2017_Q5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "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>", "tags": [], "name": "QM103_test2_2017_Q5", "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "preamble": {"css": "", "js": ""}, "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>\n<p>Give your answers as you would in Excel</p>\n<p>For example &nbsp;$-\\frac{3}{4}x^2+\\frac{5}{6}x^{-\\frac{4}{5}}-12x+4x^3e^{(2x^2-2)}$</p>\n<p>Would be entered -(3/4)*x^2 &nbsp; +(5/6)*x^(-4/5) &nbsp; -12*x &nbsp; + 4*x^3*e^(2x^2-2)</p>", "functions": {}, "parts": [{"variableReplacements": [], "marks": 0, "type": "gapfill", "gaps": [{"expectedvariablenames": ["e", "x"], "variableReplacements": [], "answer": "({c[0]}*{p[0]}*x^({p[0]}-1))*e^(x^{p[0]}+1)", "type": "jme", "vsetrange": [0, 1], "vsetrangepoints": 5, "showFeedbackIcon": true, "showpreview": true, "marks": "2", "scripts": {}, "variableReplacementStrategy": "originalfirst", "answersimplification": "all", "checkingaccuracy": 0.001, "checkvariablenames": false, "checkingtype": "absdiff", "showCorrectAnswer": true}], "prompt": "<p>$y=\\var{c[0]}e^{(x^\\var{p[0]}+1)}$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "showCorrectAnswer": true}], "variables": {"p": {"name": "p", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(2..4),5)"}, "c": {"name": "c", "description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "repeat(random(2..8),5)"}}, "extensions": [], "ungrouped_variables": ["c", "p"], "metadata": {"description": "<p>Differentiating further exponentials</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}