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Math Help - derivative

  1. #1
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    derivative

    Find derivative of f(x) = 1/(3u^2 - 1)^2

    f'(x) = (3u^2 - 1)^-2
    = (-2)(3u^2 - 1)^-3(6u)
    = -12u(3u^2 - 1)^-3
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  2. #2
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    Quote Originally Posted by becky
    Find derivative of f(x) = 1/(3u^2 - 1)^2

    f'(x) = (3u^2 - 1)^-2
    = (-2)(3u^2 - 1)^-3(6u)
    = -12u(3u^2 - 1)^-3
    You probably mean,
    y=\frac{1}{(3x^2-1)^2}
    Let,
    u=3x^2-1
    Then,
    y=\frac{1}{u^2}=u^{-2}
    Thus,
    \frac{dy}{du}=-2u^{-3}
    And,
    \frac{du}{dx}=6x
    Thus,
    \frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx}
    Which is,
    -2(6x)u^{-3}
    Substitute for u and simplify,
    -12x(3x^2-1)^{-3}
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