8. Suppose that w = x^2 - y^2 + 4z + t and x + 2z + t = 25. Show that the equations \frac{\partial w}{\partial x}=2 x-1 \quad \text { and } \quad \frac{\partial w}{\partial x}=2 x-2 each give dw/dx, depending on which variables are chosen to be dependent and which variables are chosen to be independent.Identify the independent variables in each case.

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