设 $z=z(x, y)$ 由 $\left\{\begin{array}{l}x=u e ^v, \\ y=u v,(u>0, v>1) \\ z=v\end{array}\right.$ 所确定, 则 $\frac{\partial^2 z}{\partial x \partial y}=$
$\text{A.}$ $\frac{x y}{z(1-z)^3}$.
$\text{B.}$ $\frac{x y}{z(z-1)^3}$.
$\text{C.}$ $\frac{z}{x y(1-z)^3}$.
$\text{D.}$ $\frac{z}{x y(z-1)^3}$.