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Math Help - Implicit Differentiation #2

  1. #1
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    Implicit Differentiation #2

    find dy/dx

    3x^2+4xy^3=9
    6x(dy/dx)+4y^3+4x3y^2(dy/dx)=0
    dy/dx(6x+4x3y^2)=-4y^3

    dy/dx=(-4y^3)/(12xy^2+6x)
    dy/dx=(-4y^3)/6x(2y^2+1)

    can someone check to see if this is correct?
    Last edited by mr fantastic; August 12th 2009 at 03:59 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    find dy/dx

    3x^2+4xy^3=9
    6x(dy/dx)+4y^3+4x3y^2(dy/dx)=0
    dy/dx(6x+4x3y^2)=-4y^3

    dy/dx=(-4y^3)/(12xy^2+6x)
    dy/dx=(-4y^3)/6x(2y^2+1)

    can someone check to see if this is correct?
    sorry, it's not.

    \frac{d}{dx} (3x^2 + 4xy^3 = 9)

    6x + 4x \cdot 3y^2 \frac{dy}{dx} + y^3 \cdot 4 = 0

    12xy^2 \frac{dy}{dx} = -(6x + 4y^3)

    \frac{dy}{dx} = -\frac{3x + 2y^3}{6xy^2}
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    Just in case a picture helps...



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