Answer
$$\frac{\partial f(x,y)}{\partial x}=ye^{xy}$$
$$\frac{\partial f(x,y)}{\partial y}=xe^{xy}$$
Work Step by Step
We will use chain rule to solve both partial derivatives.
The partial derivative with respect to $x$ is:
$$\frac{\partial f(x,y)}{\partial x}=\frac{\partial }{\partial x}(e^{xy})=e^{xy}\frac{\partial}{\partial x}(xy)=ye^{xy}$$
because $y$ is treated as a constant.
The partial derivative with respect to $y$ is:
$$\frac{\partial f(x,y)}{\partial y}=\frac{\partial }{\partial y}(e^{xy})=e^{xy}\frac{\partial }{\partial y}(xy)=xe^{xy}$$
because here $x$ is treated as a constant.
