已知 $x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right), \sin x=-\frac{3}{5}$, 则 $\tan 2 x=(\quad)$
$\because$ 已知 $x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right), \sin x=-\frac{3}{5}, \therefore \cos x=\sqrt{1-\sin ^{2} x}=\frac{4}{5}, \tan x=\frac{\sin x}{\cos x}=-\frac{3}{4}$,则 $\tan 2 x=\frac{2 \tan x}{1-\tan ^{2} x}=-\frac{24}{7}$, 故选: $D$.