设 $z=f(x, v), v=v(x, y)$ 其中 $f, v$ 具有二阶连续偏导数. 则 $\frac{\partial^2 z}{\partial y^2}=(\quad)$.
A
$\frac{\partial^2 f}{\partial v \partial y} \cdot \frac{\partial v}{\partial y}+\frac{\partial f}{\partial v} \cdot \frac{\partial^2 v}{\partial y^2}$;
B
$\frac{\partial f}{\partial v} \cdot \frac{\partial^2 v}{\partial y^2}$;
C
$\frac{\partial^2 f}{\partial v^2}\left(\frac{\partial v}{\partial y}\right)^2+\frac{\partial f}{\partial v} \cdot \frac{\partial^2 v}{\partial y^2}$;
D
$\frac{\partial^2 f}{\partial v^2} \cdot \frac{\partial v}{\partial y}+\frac{\partial f}{\partial v} \cdot \frac{\partial^2 v}{\partial y^2}$.
E
F