已知函数 $f(x, y)=\ln (y+|x \sin y|)$ ，则 ( )
A
$\left.\frac{\partial f}{\partial x}\right|_{(0,1)}$ 不存在, $\left.\frac{\partial f}{\partial y}\right|_{(0,1)}$ 存在
B
$\left.\frac{\partial f}{\partial x}\right|_{(0,1)}$ 存在, $\left.\frac{\partial f}{\partial y}\right|_{(0,1)}$ 不存在
C
$\left.\frac{\partial f}{\partial x}\right|_{(0,1)},\left.\frac{\partial f}{\partial y}\right|_{(0,1)}$ 均存在
D
$\left.\frac{\partial f}{\partial x}\right|_{(0,1)},\left.\frac{\partial f}{\partial y}\right|_{(0,1)}$ 均不存在
E
F