A scalar field is defined as f(x,y,z)=x2y+y2z+z2xf(x, y, z) = x^2y + y^2z + z^2xf(x,y,z)=x2y+y2z+z2x. Calculate the Laplacian ∇2f=∂2f∂x2+∂2f∂y2+∂2f∂z2\nabla^2 f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2}∇2f=∂x2∂2f+∂y2∂2f+∂z2∂2f.
2x+2y+2z2x + 2y + 2z2x+2y+2z
2y+2z+2x2y + 2z + 2x2y+2z+2x
000
2(x+y+z)2(x+y+z)2(x+y+z)