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Math Help - second derivative of e^(1/x)

  1. #1
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    second derivative of e^(1/x)

    I need help finding the second derivative of e^(1/x)

    So, f'(x) = e^(1/x) * (d/dx)(1/x)

    f'(x) = e^(1/x) * (d/dx)(1/x)
    f'(x) = -1/(x^2) * e^(1/x)

    Using the product rule where u = -1/(x^2) and v = e^(1/x)
    f''(x) = -1/(x^2) * [-1/(x^2) * e^(1/x)] + e^(1/x) * [2/(x^3)]
    f''(x) = 1/(x^4) * e^(1/x) + 2/(x^3) * e^(1/x)


    I know I am close just canít figure out the next step.
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  2. #2
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    Quote Originally Posted by nearuncertainty View Post
    I need help finding the second derivative of e^(1/x)

    So, f'(x) = e^(1/x) * (d/dx)(1/x)

    f'(x) = e^(1/x) * (d/dx)(1/x)
    f'(x) = -1/(x^2) * e^(1/x)

    Using the product rule where u = -1/(x^2) and v = e^(1/x)
    f''(x) = -1/(x^2) * [-1/(x^2) * e^(1/x)] + e^(1/x) * [2/(x^3)]
    f''(x) = 1/(x^4) * e^(1/x) + 2/(x^3) * e^(1/x)


    I know I am close just canít figure out the next step.
    You found it correctly.
    there is no next step.
    If you to solve the equation f''(x)=0.
    Start by taking e^{1/x} as a common factor.
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