Functions of two variables and partial derivatives practice question 5

Hold $x$ fixed. The function is a product of $x + y^{2}$ and $e^{xy}$, and both factors contain $y$: use the product rule.

With $x$ constant, $\dfrac{\partial}{\partial y}\left(x + y^{2}\right) = 2y$, and $\dfrac{\partial}{\partial y}e^{xy} = x\,e^{xy}$ by the chain rule.