Step 1:

The potential function is $\"\"$ .

Gradient field :

If $\"\"$ is scalar function of two variables, then the gradient vector and it is denoted by $\"\"$ is $\"\"$ .

The gradient of the function $\"\"$ is $\"\"$ .

$\"\"$ is the partial derivative of $\"\"$ with respect to $\"\"$ .

Then $\"\"$ .

$\"\"$ is the partial derivative of $\"\"$ with respect to $\"\"$ .

Then $\"\"$ .

$\"\"$

The conservative vector field is $\"\"$ .

Solution :

The gradient of $\"\"$ is $\"\"$ .

The conservative vector field is $\"\"$ .