VC3.1

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\nabla f=[i{\frac  {\partial }{\partial x}}+j{\frac  {\partial }{\partial y}}+k{\frac  {\partial }{\partial z}}](x^{3}+y^{3}+z^{3}+3xyz)\,

=i{\frac  {\partial }{\partial x}}(x^{3}+y^{3}+z^{3}+3xyz)+j{\frac  {\partial }{\partial y}}(x^{3}+y^{3}+z^{3}+3xyz)+k{\frac  {\partial }{\partial z}}(x^{3}+y^{3}+z^{3}+3xyz)\,

=i(3x^{2}+3yz)+j(3y^{2}+3xz)+k(3z^{2}+3xy)\,

=3[(x^{2}+yz)i+(y^{2}+xz)j+(z^{2}+xy)k]\,

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