If Z = 2x-y/ x+y
Find dz/dx and dz/dy
For the function z=2x−yx+yz = \frac{2x-y}{x+y}z=x+y2x−y let us find ∂z∂x\frac{\partial z}{\partial x}∂x∂z and ∂z∂y:\frac{\partial z}{\partial y}:∂y∂z:
∂z∂x=2(x+y)−(2x−y)(x+y)2=3y(x+y)2\frac{\partial z}{\partial x}=\frac{2(x+y)-(2x-y)}{(x+y)^2}=\frac{3y}{(x+y)^2}∂x∂z=(x+y)22(x+y)−(2x−y)=(x+y)23y
∂z∂y=−(x+y)−(2x−y)(x+y)2=−3x(x+y)2\frac{\partial z}{\partial y}=\frac{-(x+y)-(2x-y)}{(x+y)^2}=\frac{-3x}{(x+y)^2}∂y∂z=(x+y)2−(x+y)−(2x−y)=(x+y)2−3x
