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Thread: Implicit Differention

  1. #1
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    Implicit Differention

    Well I tried out this equation(x^3-2x^2y+3xy^2 = 38, and i got dy/dx = 4xy+3y^2/-2x^2+6xy. I know it is incorrect. Can someone walk me through this so I can correct my mistake? I'm studying for a test on monday
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  2. #2
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    $\displaystyle x^{3} -2x^{2}y +3xy^{2} =38 $

    $\displaystyle 3x^{2} - 4xy - 2x^{2} \frac {dy}{dx} + 3y^{2} + 6xy \frac {dy}{dx} = 0 $

    now solve for $\displaystyle \frac {dy}{dx} $
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    Quote Originally Posted by sgonzalez90 View Post
    Well I tried out this equation(x^3-2x^2y+3xy^2 = 38, and i got dy/dx = 4xy+3y^2/-2x^2+6xy. I know it is incorrect. Can someone walk me through this so I can correct my mistake? I'm studying for a test on monday
    $\displaystyle \frac{d}{dx}\left[x^3 - 2x^2y + 3xy^2 = 38\right]
    $

    $\displaystyle 3x^2 - 2x^2 \frac{dy}{dx} - 4xy + 6xy \frac{dy}{dx} + 3y^2 = 0$

    $\displaystyle \frac{dy}{dx}\left(6xy - 2x^2\right) = 4xy - 3x^2 - 3y^2$

    $\displaystyle \frac{dy}{dx} = \frac{4xy - 3x^2 - 3y^2}{6xy - 2x^2}$
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