设函数 $f(x)$ 连续, 若 $F(u, v)=\iint_{D_{ v }} \frac{f\left(x^2+y^2\right)}{\sqrt{x^2+y^2}} d x d y$,其中区域 $D_{ uv }$ 为图中阴影部分, 则 $\frac{\partial F}{\partial u}=$
$\text{A.}$ $v f\left(u^2\right)$.
$\text{B.}$ $\frac{v}{u} f\left(u^2\right)$.
$\text{C.}$ $v f(u)$.
$\text{D.}$ $\frac{v}{u} f(u)$.