$y = \\var{num1[0]}x^\\var{num1[1]} + \\var{num1[2]}x + x^\\var{num1[3]} + \\var{num1[4]}$
\n$\\frac{dy}{dx} =$ [[0]]
\n"}, {"adaptiveMarkingPenalty": 0, "useCustomName": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "gaps": [{"useCustomName": false, "scripts": {}, "checkVariableNames": false, "showFeedbackIcon": true, "customName": "", "type": "jme", "marks": 1, "answer": "{num2[0]}e^x + {num2[1]} + 1/x - {num2[3]} sin(x)", "checkingAccuracy": 0.001, "adaptiveMarkingPenalty": 0, "failureRate": 1, "checkingType": "absdiff", "unitTests": [], "showPreview": true, "showCorrectAnswer": true, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "vsetRange": [0, 1], "valuegenerators": [{"name": "x", "value": ""}]}], "showFeedbackIcon": true, "showCorrectAnswer": true, "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "sortAnswers": false, "prompt": "$y = \\var{num2[0]}e^x + \\var{num2[1]}x + \\ln\\var{num2[2]}x + \\var{num2[3]}\\cos (x)$
\n$\\frac{dy}{dx} =$ [[0]]
"}, {"adaptiveMarkingPenalty": 0, "useCustomName": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "gaps": [{"useCustomName": false, "scripts": {}, "checkVariableNames": false, "showFeedbackIcon": true, "customName": "", "type": "jme", "marks": 1, "answer": "{num3[0]}x^({ans31}) + {num3[1]}x^({ans32})+ {num3[2]}", "checkingAccuracy": 0.001, "adaptiveMarkingPenalty": 0, "failureRate": 1, "checkingType": "absdiff", "unitTests": [], "showPreview": true, "showCorrectAnswer": true, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "vsetRange": [0, 1], "valuegenerators": [{"name": "x", "value": ""}]}], "showFeedbackIcon": true, "showCorrectAnswer": true, "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "sortAnswers": false, "prompt": "$y = x^\\var{num3[0]} + x^\\var{num3[1]} + \\var{num3[2]}x + \\var{num3[3]}$
\n$\\frac{dy}{dx} =$ [[0]]
"}, {"adaptiveMarkingPenalty": 0, "useCustomName": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "gaps": [{"useCustomName": false, "scripts": {}, "checkVariableNames": false, "showFeedbackIcon": true, "customName": "", "type": "jme", "marks": 1, "answer": "{ans41}x^{ans42} - {ans43}x^{ans44} - {num4[5]} + {ans45}x^{-(1/2)}", "checkingAccuracy": 0.001, "adaptiveMarkingPenalty": 0, "failureRate": 1, "checkingType": "absdiff", "unitTests": [], "showPreview": true, "showCorrectAnswer": true, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "vsetRange": [0, 1], "valuegenerators": [{"name": "x", "value": ""}]}], "showFeedbackIcon": true, "showCorrectAnswer": true, "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "sortAnswers": false, "prompt": "$y = \\var{num4[0]}x^\\var{num4[1]} + \\frac{\\var{num4[2]}}{x^\\var{num4[3]}} + \\var{num4[4]} - \\var{num4[5]}x + \\var{num4[6]} \\sqrt x$
\n$\\frac{dy}{dx} =$ [[0]]
"}, {"adaptiveMarkingPenalty": 0, "useCustomName": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "gaps": [{"useCustomName": false, "scripts": {}, "checkVariableNames": false, "showFeedbackIcon": true, "customName": "", "type": "jme", "marks": 1, "answer": "{ans51}x^{ans52} + {num5[2]} + {ans53}x^{ans54} - (1/2)x^{-3/2}", "checkingAccuracy": 0.001, "adaptiveMarkingPenalty": 0, "failureRate": 1, "checkingType": "absdiff", "unitTests": [], "showPreview": true, "showCorrectAnswer": true, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "vsetRange": [0, 1], "valuegenerators": [{"name": "x", "value": ""}]}], "showFeedbackIcon": true, "showCorrectAnswer": true, "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "sortAnswers": false, "prompt": "$y = \\var{num5[0]}x^\\var{num5[1]} + \\var{num5[2]}x - \\frac{1}{\\var{num5[3]}x^\\var{num5[4]}} + \\frac{1}{\\sqrt x} - \\var{num5[5]}$
\n$\\frac{dy}{dx} =$ [[0]]
\nN.B. Put a multipication between the number and the cosine and sine functions in your answer!!
"}, {"adaptiveMarkingPenalty": 0, "useCustomName": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "unitTests": [], "gaps": [{"useCustomName": false, "scripts": {}, "checkVariableNames": false, "showFeedbackIcon": true, "customName": "", "type": "jme", "marks": 1, "answer": "{ans61}cos({num6[1]}x) - {ans62}sin({num6[3]}x)", "checkingAccuracy": 0.001, "adaptiveMarkingPenalty": 0, "failureRate": 1, "checkingType": "absdiff", "unitTests": [], "showPreview": true, "showCorrectAnswer": true, "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customMarkingAlgorithm": "", "vsetRange": [0, 1], "valuegenerators": [{"name": "x", "value": ""}]}], "showFeedbackIcon": true, "showCorrectAnswer": true, "customName": "", "variableReplacementStrategy": "originalfirst", "type": "gapfill", "marks": 0, "variableReplacements": [], "customMarkingAlgorithm": "", "sortAnswers": false, "prompt": "$y = \\var{num6[0]}\\sin \\var{num6[1]}x + \\var{num6[2]}\\cos \\var{num6[3]}x$
\n$\\frac{dy}{dx} =$ [[0]]
"}], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"num1": {"description": "", "name": "num1", "group": "Ungrouped variables", "definition": "shuffle(2..8)[0..5]", "templateType": "anything"}, "ans51": {"description": "", "name": "ans51", "group": "Ungrouped variables", "definition": "num5[0]*num5[1]", "templateType": "anything"}, "ans61": {"description": "", "name": "ans61", "group": "Ungrouped variables", "definition": "num6[0]*num6[1]", "templateType": "anything"}, "num2": {"description": "", "name": "num2", "group": "Ungrouped variables", "definition": "shuffle(2..8)[0..4]", "templateType": "anything"}, "ans7": {"description": "", "name": "ans7", "group": "Ungrouped variables", "definition": "num7[0]*num7[1]*-1", "templateType": "anything"}, "ans32": {"description": "", "name": "ans32", "group": "Ungrouped variables", "definition": "num3[1]-1", "templateType": "anything"}, "num7": {"description": "", "name": "num7", "group": "Ungrouped variables", "definition": "shuffle(2..5)[0..2]", "templateType": "anything"}, "ans41": {"description": "", "name": "ans41", "group": "Ungrouped variables", "definition": "num4[0]*num4[1]", "templateType": "anything"}, "ans31": {"description": "", "name": "ans31", "group": "Ungrouped variables", "definition": "num3[0]-1", "templateType": "anything"}, "num3": {"description": "", "name": "num3", "group": "Ungrouped variables", "definition": "shuffle(3..8)[0..4]", "templateType": "anything"}, "num4": {"description": "", "name": "num4", "group": "Ungrouped variables", "definition": "shuffle(3..12)[0..7]", "templateType": "anything"}, "ans63": {"description": "", "name": "ans63", "group": "Ungrouped variables", "definition": "num6[4]*num6[5]", "templateType": "anything"}, "ans43": {"description": "", "name": "ans43", "group": "Ungrouped variables", "definition": "num4[2]*num4[3]", "templateType": "anything"}, "ans13": {"description": "", "name": "ans13", "group": "Ungrouped variables", "definition": "num1[2]", "templateType": "anything"}, "num5": {"description": "", "name": "num5", "group": "Ungrouped variables", "definition": "shuffle(3..10)[0..6]", "templateType": "anything"}, "ans45": {"description": "", "name": "ans45", "group": "Ungrouped variables", "definition": "num4[6]/2", "templateType": "anything"}, "ans11": {"description": "", "name": "ans11", "group": "Ungrouped variables", "definition": "num1[0]*num1[1]", "templateType": "anything"}, "ans52": {"description": "", "name": "ans52", "group": "Ungrouped variables", "definition": "num5[1]-1", "templateType": "anything"}, "ans54": {"description": "", "name": "ans54", "group": "Ungrouped variables", "definition": "(num5[4]*-1)-1", "templateType": "anything"}, "ans44": {"description": "", "name": "ans44", "group": "Ungrouped variables", "definition": "(num4[3]*-1)-1", "templateType": "anything"}, "ans62": {"description": "", "name": "ans62", "group": "Ungrouped variables", "definition": "num6[2]*num6[3]", "templateType": "anything"}, "ans42": {"description": "", "name": "ans42", "group": "Ungrouped variables", "definition": "num4[1]-1", "templateType": "anything"}, "num6": {"description": "", "name": "num6", "group": "Ungrouped variables", "definition": "shuffle(3..12)[0..8]", "templateType": "anything"}, "ans14": {"description": "", "name": "ans14", "group": "Ungrouped variables", "definition": "num1[3]", "templateType": "anything"}, "ans15": {"description": "", "name": "ans15", "group": "Ungrouped variables", "definition": "num1[3]-1", "templateType": "anything"}, "vs": {"description": "", "name": "vs", "group": "Ungrouped variables", "definition": "random('$\\pi$','e')", "templateType": "anything"}, "ans12": {"description": "", "name": "ans12", "group": "Ungrouped variables", "definition": "num1[1]-1", "templateType": "anything"}, "ans53": {"description": "", "name": "ans53", "group": "Ungrouped variables", "definition": "num5[4]/num5[3]", "templateType": "anything"}}, "tags": ["rebelmaths"], "advice": "i)
\n$y = \\var{num1[0]}x^\\var{num1[1]} + \\var{num1[2]}x + x^\\var{num1[3]} + \\var{num1[4]}$
\n$\\frac{dy}{dx} = (\\var{num1[1]} \\times \\var{num1[0]})x^{\\var{num1[1]}-1} + \\var{num1[2]} + (1 \\times \\var{num1[3]})x^{\\var{num1[3]}-1}$
\n$\\var{ans11}x^(\\var{ans12}) + \\var{ans13}+ \\var{ans14}x^\\var{ans15}$
\nii)
\n$y = \\var{num2[0]}e^x + \\var{num2[1]}x + \\ln\\var{num2[2]}x + \\var{num2[3]}\\cos x$
\n$\\frac{dy}{dx} = \\var{num2[0]}e^x + \\var{num2[1]} + \\frac{1}{x} - \\var{num2[3]}\\sin x$
\niii)
\n$y = x^\\var{num3[0]} + x^\\var{num3[1]} + \\var{num3[2]}x + \\var{num3[3]}$
\n$\\frac{dy}{dx} = (1 \\times \\var{num3[0]})x^{\\var{num3[0]}-1} + (1 \\times \\var{num3[1]})x^{\\var{num3[1]}-1} + \\var{num3[2]}$
\n$\\var{num3[0]}x^\\var{ans31} + \\var{num3[1]}x^\\var{ans32}+ \\var{num3[2]}$
\niv)
\n$y = \\var{num4[0]}x^\\var{num4[1]} + \\frac{\\var{num4[2]}}{x^\\var{num4[3]}} + \\var{num4[4]} - \\var{num4[5]}x + \\var{num4[6]} \\sqrt x$
\n$\\frac{dy}{dx} = (\\var{num4[1]} \\times \\var{num4[0]})x^{\\var{num4[1]}-1} + \\var{num4[2]}x^{-\\var{num4[3]}} - \\var{num4[5]} + \\var{num4[6]}x^{\\frac{1}{2}}$
\n$(\\var{num4[1]} \\times \\var{num4[0]})x^{\\var{num4[1]}-1} + (-\\var{num4[3]} \\times \\var{num4[2]})x^{-\\var{num4[3]}-1} - \\var{num4[5]} + (\\frac{1}{2} \\times \\var{num4[6]})x^{\\frac{1}{2}-1}$
\n$\\var{ans41}x^\\var{ans42} - \\var{ans43}x^\\var{ans44} - \\var{num4[5]} + \\var{ans45}x^{-\\frac{1}{2}}$
\nv)
\n$y = \\var{num5[0]}x^\\var{num5[1]} + \\var{num5[2]}x - \\frac{1}{\\var{num5[3]}x^\\var{num5[4]}} + \\frac{1}{\\sqrt x} - \\var{num5[5]}$
\n$\\frac{dy}{dx} = (\\var{num5[1]} \\times \\var{num5[0]})x^{\\var{num5[1]}-1} + \\var{num5[2]} - \\frac{1}{\\var{num5[3]}}x^{-\\var{num5[4]}} + x^{-\\frac{1}{2}}$
\n$\\var{ans51}x^\\var{ans52} + \\var{num5[2]} + \\var{ans53}x^\\var{ans54} - \\frac{1}{2}x^{-\\frac{3}{2}}$
\nvi)
\n$y = \\var{num6[0]}\\sin \\var{num6[1]}x + \\var{num6[2]}\\cos \\var{num6[3]}x +\\var{num6[4]}e^{\\var{num6[5]}x} + \\var{num6[6]}\\ln\\var{num6[7]}x$
\n$\\frac{dy}{dx} = (\\var{num6[0]} \\times \\var{num6[1]})\\cos \\var{num6[1]}x - (\\var{num6[2]} \\times \\var{num6[3]})\\sin \\var{num6[3]}x + (\\var{num6[4]} \\times \\var{num6[5]})e^{\\var{num6[5]}x} + \\var{num6[6]} \\times \\frac{1}{x} $
\n$\\var{ans61}\\cos \\var{num6[1]}x - \\var{ans62}\\sin \\var{num6[3]}x + \\var{ans63}e^{\\var{num6[5]}x} + \\frac{\\var{num6[6]}}{x}$
\nvii)
\n$y = \\frac{\\var{num7[0]}}{e^{\\var{num7[1]}x}} + \\var{vs}$
\n$\\frac{dy}{dx} = \\var{num7[0]}e^{-\\var{num7[1]}x} + \\var{vs}$
\n$(\\var{num7[0]} \\times -\\var{num7[1]})e^{-\\var{num7[1]}x} + 0$
\n$\\var{ans7}e^(-\\var{num7[1]}x)$
", "metadata": {"description": "", "licence": "None specified"}, "functions": {}, "ungrouped_variables": ["num1", "ans11", "ans12", "ans13", "ans14", "ans15", "num2", "num3", "ans31", "ans32", "num4", "ans41", "ans42", "ans43", "ans44", "ans45", "num5", "ans51", "ans52", "ans53", "ans54", "num6", "ans61", "ans62", "ans63", "vs", "num7", "ans7"], "name": "Differentiation 5 Mix questions of the basics in differentiation ", "preamble": {"js": "", "css": ""}, "statement": "Remember the rules from questions 1 to 4:
\nFor each of the following find $\\frac{dy}{dx}$:
", "extensions": [], "variable_groups": [], "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}]}], "contributors": [{"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}