数学试题讲解

设函数

f

连续，若

F (u, v) = \iint_{D_{u v}} \frac{f (x^{2} + y^{2})}{\sqrt{x^{2} + y^{2}}} d x d y

，其中

\begin{aligned} D_{u v} : x^{2} + y^{2} = 1, x^{2} + y^{2} = u^{2}, y = 0, y = x \arctan v \\ (u > 1, v > 0) ，则 \frac{\partial F}{\partial u} = \end{aligned}

v f (u^{2})

\frac{v}{u} f (u^{2})

v f (u)

\frac{v}{u} f (u)