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Math Help - Partial Derivative?

  1. #1
    Member
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    Feb 2009
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    Partial Derivative?

    Consider the equation

    as defining implicitly as a function of and . Compute the following.

    ?

    zē + 2xz(∂z/∂x) + 4y(∂z/∂x) + (2/z)(∂z/∂x) = 0
    1 - 2(∂z/∂x) + 4(∂z/∂x) + 2(∂z/∂x) = 0
    ∂z/∂x = -1/4
    Should (∂z/∂y) answer be the same at the x? I don't get it. Please help.
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  2. #2
    Senior Member
    Joined
    Dec 2008
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    You are correct that \frac{\partial z}{\partial x}=-\frac{1}{4}. However, we will find a different answer for \frac{\partial z}{\partial y} at the same point.

    To differentiate both sides by y, we simply treat x as if it were a constant and z as if it were a function of y.
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