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Math Help - Implicit partial differentiation. Need my answer checked please

  1. #1
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    Implicit partial differentiation. Need my answer checked please

    Find \frac{\partial y}{\partial x} at the point (1,-1) for 3xy^{2}+5x^{2}y+4x=0

    So I came up with:
    (-3y^{2}\frac{\partial x}{\partial x}-6xy\frac{\partial y}{\partial x})+(10xy\frac{\partial x}{\partial x}+5x^{2}\frac{\partial y}{\partial x}+4\frac{\partial x}{\partial x})=0

    After cleaning it up a bit, I got:

    \frac{\partial y}{\partial x}(-6xy+5x^{2})=3 y^{2}-10xy-4

    =>\frac{\partial y}{\partial x}=\frac{(3 y^{2}-10xy-4)}{(-6xy+5x^{2})}

    So:

    \frac{(3 y^{2}-10xy-4)}{(-6xy+5x^{2})}|_{(1,-1)}

    =>\frac{(3 (-1)^{2}-10(1)(-1)-4)}{(-6(1)(-1)+5(1)^{2})}=\frac{9}{11}

    Can someone please double check this for me? Thanks
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  2. #2
    MHF Contributor

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    You should not have a "-" on that 3y^2 in the first line so the entire numerator in your derivative should be negative.

    Also, I do not see why you call this a "partial" derivative and use \frac{\partial y}{\partial x} rather than \frac{dy}{dx}. There does not appear to be any other independent variable.
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