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$\\frac{dy}{dx}=$ []

", "showCorrectAnswer": true, "sortAnswers": false, "type": "gapfill", "unitTests": [], "customMarkingAlgorithm": "", "scripts": {}, "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "vsetRangePoints": 5, "customMarkingAlgorithm": "malrules:\n [\n [\"(x+4x^2)*x^(x+4x^2-1)\", \"You cannot use the power rule if there is a variable in the power. Whenever you have $x$'s to the power of $x$'s, what type of differentiation must you use?\"],\n [\"1+4x+(1+8x)*ln(x)\", \"Almost there. Did you remember to multiply both sides by $y$? Remember, when you take the natural log of both sides and then differentiate both sides, the derivative of the left hand side is $\\\\frac{d}{dx} \\\\left( \\\\ln y \\\\right) = \\\\frac{1}{y} \\\\frac{dy}{dx}$, not just $\\\\frac{dy}{dx}$.\"],\n [\"y*(1+4x+(1+8x)*ln(x))\", \"Almost there. Numbas needs you to type in the actual function for $y$ i.e. enter $x^{x+4x^2}$ instead of $y$.\"]\n ]\n\n\nparsed_malrules: \n map(\n [\"expr\":parse(x),\"feedback\":x],\n x,\n malrules\n )\n\nagree_malrules (Do the student's answer and the expected answer agree on each of the sets of variable values?):\n map(\n len(filter(not x ,x,map(\n try(\n resultsEqual(unset(question_definitions,eval(studentexpr,vars)),unset(question_definitions,eval(malrule[\"expr\"],vars)),settings[\"checkingType\"],settings[\"checkingAccuracy\"]),\n message,\n false\n ),\n vars,\n vset\n )))$\\frac{dy}{dx} \\bigg|_{(1,1)} =$ []

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Logarithmic differentiation question with customised feedback to catch some common errors.

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Find the gradient of the curve $y=x^{x+4x^2}$ at the point $(1,1)$.

", "type": "question", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}]}