Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 780: 3

$\frac{\partial}{\partial y} \frac{y}{x+y}=\frac{x}{(x+y)^2}$

$\frac{\partial}{\partial y} \frac{y}{x+y}=\frac{(x+y)*\frac{\partial}{\partial y}y-y*\frac{\partial}{\partial y}(x+y)}{(x+y)^2}$ $=\frac{(x+y)*1-y*1}{(x+y)^2}$ $=\frac{x+y-y}{(x+y)^2}$ $=\frac{x}{(x+y)^2}$