Transform the equation changing to new independent variables $(u ; v)$ :
(a) $z_{t t}=a^{2} z_{x x}, u=x-a t, v=x+a t$
(b) $x^{2} z_{x x}-y^{2} z_{y y}=0, u=x y, v=\frac{y}{x}$
I understand how to perform this by chain rule to $u_x$, but with second derivative I have no idea.