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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