// Numbas version: exam_results_page_options {"name": "Power rule 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "statement": "

Differentiate the following:

\n

\$$y=\\var{a1}x^{\\var{a2}}+\\var{b1}x^{\\var{b2}}+\\var{c1}\$$

", "variable_groups": [], "ungrouped_variables": ["a1", "a2", "b1", "b2", "c1"], "variables": {"b1": {"group": "Ungrouped variables", "description": "", "definition": "random(2 .. 14#1)", "name": "b1", "templateType": "randrange"}, "a2": {"group": "Ungrouped variables", "description": "", "definition": "random(5 .. 12#1)", "name": "a2", "templateType": "randrange"}, "b2": {"group": "Ungrouped variables", "description": "", "definition": "random(1 .. 5#1)", "name": "b2", "templateType": "randrange"}, "a1": {"group": "Ungrouped variables", "description": "", "definition": "random(2 .. 10#1)", "name": "a1", "templateType": "randrange"}, "c1": {"group": "Ungrouped variables", "description": "", "definition": "random(3 .. 18#1)", "name": "c1", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Power rule

"}, "parts": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "customName": "", "prompt": "

\$$\\frac{dy}{dx}=\$$ [[0]]

", "showCorrectAnswer": true, "sortAnswers": false, "gaps": [{"failureRate": 1, "variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": 1, "customMarkingAlgorithm": "", "vsetRangePoints": 5, "customName": "", "answer": "{a1}*{a2}*x^{{a2}-1}+{b1}*{b2}*x^{{b2}-1}", "showCorrectAnswer": true, "checkingAccuracy": 0.001, "checkVariableNames": false, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "type": "jme", "vsetRange": [0, 1], "useCustomName": false, "showFeedbackIcon": true, "showPreview": true, "valuegenerators": [{"value": "", "name": "x"}], "variableReplacements": [], "scripts": {}}], "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "showFeedbackIcon": true, "variableReplacements": [], "scripts": {}}], "advice": "

Apply the rule:

\n

\$$y=ax^n\\,\\,\\,then\\,\\,\\,\\frac{dy}{dx}=nax^{n-1}\$$

\n

In this example

\n

\$$y=\\var{a1}x^{\\var{a2}}+\\var{b1}x^{\\var{b2}}+\\var{c1}\$$

\n

\$$\\frac{dy}{dx}=\\var{a2}*\\var{a1}x^{\\var{a2}-1}+\\var{b2}*\\var{b1}x^{\\var{b2}-1}\$$

\n

\$$\\frac{dy}{dx}=\\simplify{{a2}*{a1}x^{{a2}-1}+{b2}*{b1}x^{{b2}-1}}\$$

", "functions": {}, "rulesets": {}, "extensions": [], "name": "Power rule 1", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Kamila Yusufu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2554/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Katy Dobson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/854/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Kamila Yusufu", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2554/"}]}