Answer
$\phi(x, y)=\lt \dfrac{1}{y}, \dfrac{ -x}{y^2} \gt$
Work Step by Step
Our aim is to compute the gradient vector field.
We are given that $\phi(x, y)=\lt \dfrac{x}{y} \gt$
or, $=\lt \dfrac{\partial (\dfrac{x}{y} ) }{\partial x}, \dfrac{\partial ( \dfrac{x}{y} ) }{\partial y}\gt$
or, $=\lt \dfrac{1}{y} \times \dfrac{\partial x}{\partial x}, x \times \dfrac{\partial (1/y) }{\partial y} \gt$
Thus, our required result is: $\phi(x, y)=\lt \dfrac{1}{y}, \dfrac{ -x}{y^2} \gt$
