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23 July, 19:47

Finding Higher-Order Derivatives In Exercise, find the second derivative of the function.

f (x) = 2 + x3 ln x

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  1. 23 July, 20:12
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    d^2y/dx^2 = 5x + 6x lnx

    Step-by-step explanation:

    f (x) = y = 2 + x^3 lnx

    Differentiating a constant (2) = 0

    Differentiating x^3 lnx = x^3 (1/x) + lnx (3x^2) = x^2 + 3x^2 lnx

    dy/dx = 0 + x^2 + 3x^2 lnx = x^2 + 3x^2 lnx

    Differentiating x^2 = 2x

    Differentiating 3x^2 lnx = 3x^2 (1/x) + lnx (6x) = 3x + 6x lnx

    d^2y/dx^2 = 2x + 3x + 6x lnx = 5x + 6x lnx
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