Partial derivatives in terms of both variables

Question

if i have a scalar function as below, i know how to find the partial derivative in terms of x, but can someone gives me some help in understanding how i can take the partial derivative in terms of both variables? Any help is appreciated, thanks in advance

f(x, y) = sin(xy)

Answer 1

$$\frac{\partial f}{\partial x} = \cos(xy)\left(\frac{\partial}{\partial x}xy\right) = y\cos(xy)$$

$$\frac{\partial f}{\partial y} = \cos(xy)\left(\frac{\partial}{\partial y}xy\right) = x\cos(xy)$$