Question

If Z = 2x-y/ x+y

Find dz/dx and dz/dy

Answer 1

For the function $z = \frac{2x-y}{x+y}$ let us find $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}:$

$\frac{\partial z}{\partial x}=\frac{2(x+y)-(2x-y)}{(x+y)^2}=\frac{3y}{(x+y)^2}$

$\frac{\partial z}{\partial y}=\frac{-(x+y)-(2x-y)}{(x+y)^2}=\frac{-3x}{(x+y)^2}$