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Math Help - Find g'(x) and g"(x)

  1. #1
    Senior Member nycmath's Avatar
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    Find g'(x) and g"(x)

    I need to find the first and second derivative of
    g(x) = (e^x)/x.

    I found g'(x) to be e^x(x-1)/(x^2).

    I then found g"(x) to be (e^x)/x^3 but the book's answer is more involved.

    According to the book, the complete answer is
    (e^x)/(x^3) times (x^2-2x+2).

    Where does the trinomial come from?
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  2. #2
    Forum Admin topsquark's Avatar
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    Re: Find g'(x) and g"(x)

    Quote Originally Posted by nycmath View Post
    I need to find the first and second derivative of
    g(x) = (e^x)/x.

    I found g'(x) to be e^x(x-1)/(x^2).

    I then found g"(x) to be (e^x)/x^3 but the book's answer is more involved.

    According to the book, the complete answer is
    (e^x)/(x^3) times (x^2-2x+2).

    Where does the trinomial come from?
    Without seeing your work I can only guess. However it's probably here:
    Write your first derivative as:
    g'(x) = \frac{x - 1}{x^2} \cdot e^x = \frac{1}{x} \cdot e^x - \frac{1}{x^2} \cdot e^x

    and try it again.

    -Dan
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  3. #3
    Senior Member nycmath's Avatar
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    Re: Find g'(x) and g"(x)

    I was able to find the second derivative after a third try.
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