Final answer:
The gradient of the function f(x, y) = xy is (y, x).
Step-by-step explanation:
To find the gradient of the function f(x, y) = xy, we need to determine the partial derivatives ∂f/∂x and ∂f/∂y. Taking the partial derivative of f with respect to x, keeping y constant, we get ∂f/∂x = y. Similarly, taking the partial derivative of f with respect to y, keeping x constant, we get ∂f/∂y = x. Therefore, the gradient of f is the vector (∂f/∂x, ∂f/∂y) = (y, x).