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Math Help - derivative

  1. #1
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    derivative

    trying to get the second derivative from this
    f'(x)=-[{e^{x}(x-2)}/{(x-1)^{2}}]
    been using the quotient rule but answer differs from book
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  2. #2
    Super Member Aryth's Avatar
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    Alright, using the quotient rule you should get that:

    f''(x) = -\frac{2(x - 1)e^x(x - 2) - [e^x(x - 2) + e^x](x - 1)^2}{(x - 1)^4}

    Note: In the second term in the numerator you have to separately use the product rule or this will not come out right.

    f''(x) = -\frac{2(x -1)e^x(x - 2) - e^x(x - 1)^3}{(x - 1)^4}

    From here you can simplify it however you like, but here is an option:

    f''(x) = -\frac{e^x[2(x - 2) - (x - 1)^2]}{(x - 1)^3} = -\frac{e^x(x+5)}{(x - 1)^2}
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