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25 October, 23:14

Find the second derivative y = x^2lnx

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  1. 25 October, 23:56
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    First we use product rule

    y=x^2lnx

    dy/dx = x^2 d/dx (lnx) + lnx d/dx (x^2)

    dy/dx = x^2 (1/x) + lnx (2x)

    dy/dx = x + 2xlnx

    now taking second derivative:

    d2y/dx2 = 1 + 2[x (1/x) + lnx (1) ]

    d2y/dx2 = 1 + 2[1+lnx]

    1+2+2lnx

    3+2lnx is the answer
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