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16 September, 14:12

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

f (x) = ln x/x^3 + x

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  1. 16 September, 14:18
    0
    d^2y/dx^2 = 2/x^2

    Step-by-step explanation:

    f (x) = y = In x/x^3 + x

    Differentiating x/x^3 = [x^3 (1) - x (3x^2) ] / (x^3) ^2 = (x^3 - 3x^3) / x^6 = - 2x^3/x^6 = - 2/x^3

    Assuming u = x/x^3

    In x/x^3 = In u

    Differentiating In u = 1/u = x^3/x = x^2

    Differentiating x = 1

    dy/dx = x^2 (-2/x^3) + 1 = - 2/x + 1

    Differentiating - 2/x = 2/x^2

    Differentiating a constant (1) = 0

    d^2y/dx^2 = 2/x^2 + 0 = 2/x^2
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