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Math Help - Need help with a derivitive problem

  1. #1
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    Need help with a derivitive problem

    I'm getting lost in the algebra. Can somebody please help me!
    I'm trying to get a derivitive of:

    x(x^2-6x+16)/(x-2)^3

    I've gotten this far:

    (x-2)^3(2x-6)-(x^2-6x+16)3(x-2)/((x-2)^2)^3

    This is where I get lost.
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  2. #2
    Senior Member Peritus's Avatar
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    Nov 2007
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    no need to get lost, the important thing is to bring the expression to a convenient form:

    f(x) = x(x^2-6x+16)/(x-2)^3 = (x^3 - 6x^2 + 16x) / (x-2)^3 =
    = (x^3 -6x^2 + 16x)*(x-2)^-3

    now as you know d/dx(a(x)*b(x)) = a '(x)*b(x) + a(x)*b '(x)
    in the present case a(x) = (x^3 -6x^2 + 16x) , b(x) = (x-2)^-3

    f '(x) = (3x^2-12x+16)/(x-2)^3 -3*(x^3 - 6x^2 + 16x)/(x-2)^4
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  3. #3
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    Smile

    Thank you so much for your help. I think I've got it now.
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