// Numbas version: finer_feedback_settings
{"name": "Leicester: Differentiation 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Leicester: Differentiation 1", "tags": ["differentiation", "fractional powers", "negative powers", "powers"], "advice": "", "rulesets": {"std": ["all", "fractionNumbers"]}, "parts": [{"prompt": "\n      <p>$f(x)=\\var{a}x^{\\var{b}}$</p>\n        <p>$\\displaystyle \\frac{df}{dx}=\\;$[[0]]</p>\n      ", "gaps": [{"notallowed": {"message": "<p>Input all numbers as fractions or integers, not as decimals.</p>", "showstrings": false, "strings": ["."], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "{a*b}*x^{b-1}", "type": "jme"}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n      <p>$f(x)=\\var{a}x^{\\var{b}}+\\var{c}x^{1/\\var{d}}$</p>\n        <p>$\\displaystyle \\frac{df}{dx}=\\;$[[0]]</p>\n      ", "gaps": [{"notallowed": {"message": "<p>Input all numbers as fractions or integers, not as decimals.</p>", "showstrings": false, "strings": ["."], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [1.0, 2.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 1.0, "answer": "{a*b}*x^{b-1}+{c}/{d}*x^({1-d}/{d})", "type": "jme"}], "type": "gapfill", "marks": 0.0}, {"prompt": "\n      <p>$\\displaystyle f(x)=\\frac{\\var{a}}{x^{1/\\var{c}}}+ \\frac{\\var{b}}{x^{-1/\\var{d}}}+\\var{ee}&nbsp;$</p>\n        <p>$\\displaystyle \\frac{df}{dx}=\\;$[[0]]</p>\n      ", "gaps": [{"notallowed": {"message": "<p>Input all numbers as fractions or integers, not as decimals.</p>", "showstrings": false, "strings": ["."], "partialcredit": 0.0}, "checkingaccuracy": 0.001, "vsetrange": [1.0, 2.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std,!noLeadingMinus", "marks": 1.0, "answer": "-{a}/{c}*x^(-{c+1}/{c})+{b}/{d}x^({1-d}/{d})", "type": "jme"}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "\n  <p>Differentiate the following functions $f(x)$ with respect to $x$.</p>\n    <p>Input all numbers as fractions or integers, not as decimals.</p>\n  ", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(2..9)", "name": "a"}, "c": {"definition": "random(2..9)", "name": "c"}, "b": {"definition": "random(2..9)", "name": "b"}, "d": {"definition": "random(2..9)", "name": "d"}, "f": {"definition": "random(2..9)", "name": "f"}, "ee": {"definition": "random(0..10)", "name": "ee"}}, "metadata": {"notes": "", "description": "<p>Differentiate $\\displaystyle ax^b, ax^b+cx^{1/d}, \\frac{a}{x^{1/c}}+\\frac{b}{x^{-1/d}}+c$ with respect to $x$.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}