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Find the Gradient Vector Field of the Scalar Function ff (That Is, Find the Conservative Vector Field

Question 67

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Find the gradient vector field of the scalar function ff . (That is, find the conservative vector field F\mathbf { F } for the potential function ff of F\mathbf { F } .)
f(x,y,z)=8xy2+2yz3f ( x , y , z ) = 8 x y ^ { 2 } + 2 y z ^ { 3 }

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