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Math Help - where are my mistakes? (basic derivatives)

  1. #1
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    where are my mistakes? (basic derivatives)

    1. y = 6x^5 + 12x^3 + 9x^2 + sqrt(pi^5)

    y' = 30x^4 + 36x^2 + 18x ... factor out a 6 -----> y' = 5x^4 + 6x^2 + 3x

    ----------------------------------------------------------------------------------------------------------------------------------------------------------------

    2. y = (x^2 + 1)^3 * (x^3 - 1)^2

    use u*dv + v*du -----> (x^2 + 1)^3 * (2)(x^3 - 1)(3x^2) + (x^3 - 1)^2 * (3)(x^2 + 1)^2 (2x)

    (6x^2) (x^3 - 1) (x^2 + 1)^3 + (6x) (x^3 - 1)^2 (x^2 + 1)^2

    (6x) (x^3 - 1) (x^2 + 1)^2 [(x^3 - 1) + (x^2 + 1) (x)

    (6x) (x^3 - 1) (x^2 + 1)^2 (2x^3 + x - 1)

    ----------------------------------------------------------------------------------------------------------------------------------------------------------------

    3. y = (x^3 + 1)/(x^3 - 2)

    use low * d.high - high * d.low / low^2

    y' = [(x^3 - 2) (3x^2) - ( x^3 + 1) (3x^2)] / (x^3 - 2)^2

    (3x^5 - 6x^2 - 3x^5 + 3x^2) / (x^3 - 2)^2

    -3x^2 / (x^3 - 2)^2

    ----------------------------------------------------------------------------------------------------------------------------------------------------------------

    4. y = x^2 * sqrt(x + 1)

    this one is giving me the most trouble i think...

    y' = (x^2) [ 1 / (2x + 2) + 2x(sqrt(x+1))

    y' = x^2 / (2x + 2) + 2x(sqrt(x+1)) ... get stuck here.
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  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
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    Jordan
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    Quote Originally Posted by golfman44 View Post
    1. y = 6x^5 + 12x^3 + 9x^2 + sqrt(pi^5)

    y' = 30x^4 + 36x^2 + 18x ... factor out a 6 -----> y' = 5x^4 + 6x^2 + 3x

    ------------------------------------------------------------------

    2. y = (x^2 + 1)^3 * (x^3 - 1)^2

    use u*dv + v*du -----> (x^2 + 1)^3 * (2)(x^3 - 1)(3x^2) + (x^3 - 1)^2 * (3)(x^2 + 1)^2 (2x)

    (6x^2) (x^3 - 1) (x^2 + 1)^3 + (6x) (x^3 - 1)^2 (x^2 + 1)^2

    (6x) (x^3 - 1) (x^2 + 1)^2 [(x^3 - 1) + (x^2 + 1) (x)

    (6x) (x^3 - 1) (x^2 + 1)^2 (2x^3 + x - 1)

    ------------------------------------------------------------------------

    3. y = (x^3 + 1)/(x^3 - 2)

    use low * d.high - high * d.low / low^2

    y' = [(x^3 - 2) (3x^2) - ( x^3 + 1) (3x^2)] / (x^3 - 2)^2

    (3x^5 - 6x^2 - 3x^5 + 3x^2) / (x^3 - 2)^2

    -3x^2 / (x^3 - 2)^2

    ------------------------------------------------------------------
    4. y = x^2 * sqrt(x + 1)

    this one is giving me the most trouble i think...

    y' = (x^2) [ 1 / (2x + 2) + 2x(sqrt(x+1))

    y' = x^2 / (2x + 2) + 2x(sqrt(x+1)) ... get stuck here.

    4) y=x^2 \sqrt{x+1}

    y'= 2x\sqrt{x+1} + x^2\left(\frac{1}{2\sqrt{x+1}}\right)

    you derived other questions correctly
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