Given f(x,y)=ln(x2+y2)f(x, y) = \ln(x^2 + y^2)f(x,y)=ln(x2+y2), determine the Laplacian Δf=∂2f∂x2+∂2f∂y2\Delta f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2}Δf=∂x2∂2f+∂y2∂2f for (x,y)≠(0,0)(x, y) \neq (0, 0)(x,y)=(0,0).
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2x2+y2\frac{2}{x^2+y^2}x2+y22
4x2+y2\frac{4}{x^2+y^2}x2+y24
4(x2+y2)2\frac{4}{(x^2+y^2)^2}(x2+y2)24