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The tangent plane of a function z=f(x,y) at point (x_0,y_0) is equal to

z-z_0=\frac{\part f}{\part x}(x-x_0)+\frac{\part f}{\part y}(y-y_0)
z=\frac{\part f}{\part x}(x-x_0)+\frac{\part f}{\part y}(y-y_0)+z_0

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