Differentiating a multivariable function Knowing that $$z(x,y)=f(\frac{x}{y})$$I'm supposed to find $$x\frac{\partial z}{\partial x} + y\frac{\partial z}{\partial y}$$ .
This problem makes no sense to me, can anyone help with the differentiation ? I really don't get how to apply the chain rule this time .

$$\frac{\partial z}{\partial x} = \frac{1}{y}f'(x/y)$$
and 
$$\frac{\partial z}{\partial y} = -\frac{x}{y^2}f'(x/y)$$
by the chain rule. All together:
$$x\frac{\partial z}{\partial x} + y\frac{\partial z}{\partial z} = \left(\frac{x}{y} - \frac{x}{y}\right)f'(x/y) = 0$$
