Question

Determine whether the vector function is a gradient and, if so, find all functions ff with that gradient.

(y2z3+1)i+(2xyz3+y)j+(3xy2z2+1)k\left(y^2 z^3+1\right) \mathbf{i}+\left(2 x y z^3+y\right) \mathbf{j}+\left(3 x y^2 z^2+1\right) \mathbf{k}

Solution

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Determine whether or not the vector function is a gradient. If so, find all the functions with that gradient. \text{\textcolor{#640000}{Determine whether or not the vector function is a gradient. If so, find all the functions with that gradient. \\ }}

(y2z3+1)i+(2xyz3+y)j+(3xy2z2+1)k.\textcolor{#000764}{ (y^2z^3 + 1) i + (2xyz^3 + y) j + (3xy^2z^2 + 1) k.}

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