Find a potential f for the vector function v = [$ye^x, e^x, z^2$]. Find a potential f for the vector function v =$ [ye^x, e^x, z^2]$ Is the answer to this question f = $[ye^x,0,2z]$ ?

$$ \
abla \phi = \mathbf{F} = \left[ \begin{array}{c} \partial_{x} \phi \\\ \partial_{y} \phi \\\ \partial_{z} \phi \end{array} \right] = \left[ \begin{array}{c} y e^{x} \\\ e^{x} \\\ z^{2} \end{array} \right] $$ The potential function is $$ \phi (x, y, z) = ye^{x} + \frac{1}{3}z^{3}, $$ modulo some constant.