Given a function: z(x,y) = 2x +2y^2(adsbygoogle = window.adsbygoogle || []).push({});

Determine ∂x/∂y [the partial differentiation of x with respect to y],

Method 1:

x = (z/2) - y^2

∂x/∂y = -2y

Method 2:

∂z/∂x = 2

∂z/∂y = 4y

∂x/∂y = ∂x/∂z X ∂z/∂y = (1/2) X 4y = 2y

One or both of these is wrong. Can someone point out where I went wrong? I started to wonder why this was happening as I was looking over some fluid mechanics problems (above problem is unrelated to my original problem but if I understand the above problem it will help)

Thanks

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# Partial differentiation with 3 variables

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