VC3.4

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Given \phi (x,y,z)=(3r^2-4r^{\frac{1}{2}}+6r^{-\frac{1}{3}}\, [1]

Let r=xi+yj+zk\, so that r^2=|r|^2=x^2+y^2+z^2\, [2]

Since PHI is function of r only,we have

\nabla \phi=\frac{\partial \phi}{\partial r}\nabla r=(6r-2r^{-\frac{1}{2}}-2r^{-\frac{4}{3}})(\frac{1}{r})r\,

=(6r-2r^{-\frac{3}{2}}-2r^{-\frac{7}{2}})=2r(3-2r^{-\frac{3}{2}}-2r^{-\frac{7}{3}})\,

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