// Numbas version: finer_feedback_settings
{"name": "Harry's copy of Differentiation 7 - Exponentials", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "rulesets": {}, "parts": [{"gaps": [{"checkingaccuracy": 0.001, "marks": "2", "scripts": {}, "showCorrectAnswer": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "type": "jme", "answer": "({c[0]}*{p[0]}*x^({p[0]}-1))*e^(x^{p[0]}+1)", "variableReplacements": [], "checkvariablenames": false, "checkingtype": "absdiff", "showpreview": true, "expectedvariablenames": ["e", "x"], "vsetrange": [0, 1], "answersimplification": "all"}], "prompt": "<p>$y=\\var{c[0]}e^{x^\\var{p[0]}+1}$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}, {"gaps": [{"checkingaccuracy": 0.001, "marks": "2", "scripts": {}, "showCorrectAnswer": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "type": "jme", "answer": "({c[2]}*{p[2]}*x^({p[2]}-1))*e^(x^{p[2]})+{c[3]}e^x", "variableReplacements": [], "checkvariablenames": true, "checkingtype": "absdiff", "showpreview": true, "expectedvariablenames": ["e", "x"], "vsetrange": [0, 1], "answersimplification": "all"}], "prompt": "<p>$y=\\var{c[2]}e^{x^\\var{p[2]}}+\\var{c[3]}e^x$</p>\n<p>$\\frac{dy}{dx}=$&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "type": "gapfill"}], "preamble": {"css": "", "js": ""}, "type": "question", "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": "Harry's copy of Differentiation 7 - Exponentials", "metadata": {"notes": "", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Differentiating further exponentials</p>"}, "variables": {"p": {"definition": "repeat(random(2..4),5)", "name": "p", "group": "Ungrouped variables", "templateType": "anything", "description": ""}, "c": {"definition": "repeat(random(2..8),5)", "name": "c", "group": "Ungrouped variables", "templateType": "anything", "description": ""}}, "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "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>", "ungrouped_variables": ["c", "p"], "variable_groups": [], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}]}], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}