Use the product rule to differentiate the function $f(x)=\\left( x^3-\\frac{1}{x} \\right)e^x$.

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", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "2", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "malrules:\n [\n [\"(3x^2+1/x^2)*e^x\", \"Note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule.\"],\n [\"(x^3-1/x)*e^x+3x^2*e^x\", \"Almost there! Double check how to correctly differentiate $\\\\frac{1}{x}$.\"],\n [\"3x^2*e^x\", \"There are a couple of things to watch here. Firstly, note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule. Secondly, double check how to correctly differentiate $\\\\frac{1}{x}$.\"],\n [\"(x^3-1/x)*e^x+(3x^2-ln(x))*e^x\", \"Almost there! Double check how to correctly differentiate $\\\\frac{1}{x}$.\"],\n [\"(x^3-1/x)*e^x+(3x^2-1/x^2)*e^x\", \"Almost there! Double check how to correctly differentiate $x^3 - \\\\frac{1}{x}$.\"],\n [\"(3x^2-1/x^2)*e^x\", \"Note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule.\"],\n [\"(3x^2+x^(-1))*e^x\", \"Note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule.\"],\n [\"(3x^2-x^(-1))*e^x\", \"Note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule.\"],\n [\"(x^3-1/x)*e^x+(3x^2-x^(-1))*e^x\", \"Almost there! Double check how to correctly differentiate $\\\\frac{1}{x}$.\"],\n [\"(3x^2+1/x^2)*x*e^(x-1)\", \"Note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule. Also, be careful when differentiating $e^x$. You cannot use the power rule for this.\"],\n [\"(x^3-1/x)*x*e^(x-1)+3x^2*e^x\", \"Double check how to correctly differentiate $\\\\frac{1}{x}$. Also, be careful when differentiating $e^x$. You cannot use the power rule for this.\"],\n [\"3x^2*x*e^(x-1)\", \"There are a few things to watch here. Firstly, note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule. Secondly, double check how to correctly differentiate $\\\\frac{1}{x}$. Also, be careful when differentiating $e^x$. You cannot use the power rule for this.\"],\n [\"(x^3-1/x)*x*e^(x-1)+(3x^2-ln(x))*e^x\", \"A couple of things to check. Double check how to correctly differentiate $\\\\frac{1}{x}$. Also, be careful when differentiating $e^x$. You cannot use the power rule for this.\"],\n [\"(x^3-1/x)*x*e^(x-1)+(3x^2-1/x^2)*e^x\", \"A couple of things to check. Double check how to correctly differentiate $x^3 - \\\\frac{1}{x}$. Also, be careful when differentiating $e^x$. You cannot use the power rule for this.\"],\n [\"(3x^2-1/x^2)*x*e^(x-1)\", \"Note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule. Also, be careful when differentiating $e^x$. You cannot use the power rule for this.\"],\n [\"(3x^2+x^(-1))*x*e^(x-1)\", \"Note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule. Also, be careful when differentiating $e^x$. You cannot use the power rule for this.\"],\n [\"(3x^2-x^(-1))*x*e^(x-1)\", \"Note that the function you need to differentiate is $\\\\left( x^3 - \\\\frac{1}{x} \\\\right) \\\\times e^x$ i.e. one function of $x$ multiplied by another function of $x$. Therefore, you need the product rule. Also, be careful when differentiating $e^x$. You cannot use the power rule for this.\"],\n [\"(x^3-1/x)*x*e^(x-1)+(3x^2-x^(-1))*e^x\", \"Double check how to correctly differentiate $\\\\frac{1}{x}$. Also, be careful when differentiating $e^x$. You cannot use the power rule for this.\"]\n ]\n\nparsed_malrules: \n map(\n [\"expr\":parse(x[0]),\"feedback\":x[1]],\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 )))