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Math Help - How did they get second derivative

  1. #1
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    How did they get second derivative

    I know the answer, but I just need a little help getting it.

    It's all in here:
    http://i44.tinypic.com/o7r6yv.jpg

    Thanks so much!
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by janedoe View Post
    I know the answer, but I just need a little help getting it.

    It's all in here:
    http://i44.tinypic.com/o7r6yv.jpg

    Thanks so much!

    Differentiate \frac{8-3t^2}{(8+t^2)^3} = (8-3t^2)(8+t^2)^{-3}

    The derivative is:

    -6t (8+t^2)^{-3} + (8-3t^2)(-3)(2t)(8+t^2)^{-4}

    Put in common denominator:

    \frac{-6t(8+t^2)}{(8+t^2)^4} + \frac{-6t(8-3t^2)}{(8+t^2)^4}=
    \frac{-48t-6t^3-48t+18t^3}{(8+t^2)^4} =
    \frac{-96t+12t^3}{(8+t^2)^4}=
    \frac{-12t(8-t^2)}{(8+t^2)^4}

    Good luck!
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  3. #3
    Super Member Random Variable's Avatar
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     S''(t) = \frac {80000*(8+t^{2})^{2} - 80000t*2(8+t^{2})2t}{(8+t^{2})^{4}} = \frac {80000(8+t^{2})\Big((8+t^{2})-4t^{2}\Big)}{(8+t^{2})^{4}}

     = \frac {80000(8-3t^{2})}{(8+t^{2})^{3}}
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