// Numbas version: exam_results_page_options {"name": "Jinhua'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": [{"functions": {}, "ungrouped_variables": ["c", "p"], "name": "Jinhua's copy of Differentiation 7 - Exponentials", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "

With these questions, the chain rule is carried out twice.

\n

They are essentially the same as the questions in 'Differentiation 6 - Exponentials', but instead of being, say, $e^{2x}$, they are something more like $e^{x^2}$.

\n

Exactly the same method is carried out.

\n

Firstly, differentiate the power of $e$. In this case, we differentiate $x^2$ to get $2x$.

\n

Now times this result by the coefficient (the coefficient here being $1$), to get a final result of:

\n

$2xe^{x^2}$

", "rulesets": {}, "parts": [{"prompt": "

$y=\\var{c[0]}e^{x^\\var{p[0]}+1}$

\n

$\\frac{dy}{dx}=$ [[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["e", "x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({c[0]}*{p[0]}*x^({p[0]}-1))*e^(x^{p[0]}+1)", "marks": "2", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "

$y=\\var{c[2]}e^{x^\\var{p[2]}}+\\var{c[3]}e^x$

\n

$\\frac{dy}{dx}=$ [[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": ["e", "x"], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "all", "scripts": {}, "answer": "({c[2]}*{p[2]}*x^({p[2]}-1))*e^(x^{p[2]})+{c[3]}e^x", "marks": "2", "checkvariablenames": true, "checkingtype": "absdiff", "type": "jme"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "

Differentiate the following.

\n

You will need to use the chain rule within these questions.

\n

Do not write out $dy/dx$; only input the differentiated right hand side of each equation.

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"p": {"definition": "repeat(random(2..4),5)", "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": "

Differentiating further exponentials

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Jean jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}]}], "contributors": [{"name": "Jean jinhua Mathias", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/353/"}]}