if y=x^e^-x^2,find dy/dx

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Please find below the solution to the asked query:

We have:y=xe-x2Taking log on both sides, we get,lny=lnxe-x2lny=e-x2.lnx    As lnmn=n.lnmDifferentiating both sides with respect to x and employing product rule, we get,1y.dydx=e-x2.ddxlnx+lnx.ddxe-x21y.dydx=e-x2x+lnxe-x2.-2x1y.dydx=e-x21x-2xlnxdydx=y.e-x21-2x2lnxxdydx=xe-x2.e-x21-2x2lnxx Answer

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