We have been provided with:
$$Z=xf(y/x)+yg(y/x), $$
and been asked to obtain $Z_{xx},\ Z_{xy}$ and $ Z_{yy}$.
I am well aware that I will be differentiating $Z$ with respect to $x$. I've been provided with an answer from a group member but the working out is very lacking, hence I am quite stuck.
$$Z_x=y/(x+y)^2.$$
What has been done to achieve this?
From the given information we obtain
$$Z=xf(y/x)+yg(y/x)\implies Z_x=f(y/x)+xf_x(y/x)\frac{-y}{x^2}+yg_x(y/x)\frac{-y}{x^2}=\\=f(y/x)-\frac{y}xf_x(y/x)-\frac{y^2}{x^2}g_x(y/x)$$