Final answer:
The derivative of the function f(x, y) = xy is found by taking partial derivatives with respect to x and y, yielding the gradient (∂f/∂x, ∂f/∂y) = (y, x).
Step-by-step explanation:
You asked about finding the derivative of the function f(x, y) = xy. This involves partial differentiation since the function has two variables, x and y. The derivative of a function in two variables is given by a gradient, which is a vector of partial derivatives with respect to each variable in the function. In your case, the partial derivative of f with respect to x would be y because the derivative of x times y with respect to x is y. Similarly, the partial derivative of f with respect to y would be x since the derivative of x is simply 1. Therefore, the gradient of f(x, y) is given as (∂f/∂x, ∂f/∂y) = (y, x)