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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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