Determine Whether or Not Vector Field Is Conservative $f$ Such That $\mathbf { F } = \nabla f$

Short Answer

Determine whether or not vector field is conservative. If it is conservative, find a function $f$ such that $\mathbf { F } = \nabla f$ .
$$\mathbf { F } ( x , y , z ) = 25 y z e ^ { 5 x x _ { i } } \mathbf { i } + 5 e ^ { 5 x x _ { j } } \mathbf { j } + 25 x y e ^ { 5 x z } \mathbf { k }$$