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A curve is defined by the equation x^2y^3+4x+2y=12. Find dy/dx in terms of x and y.

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    x^2y^3+4x+2y=12

    use the product rule as needed:

    2x y^3 + 3x^2y^2 y' + 4 + 2y' = 0
    y'(3x^2 y^2 + 2) = -2xy^3 - 4

    y' is thus

    -2(xy^3 + 2)
    -------------
    3x^2 y^2 + 2

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