Prove that $\displaystyle \frac{d}{dx} \arcsin x=\frac{1}{\sqrt{1-x^2}}$

Given that the variables x and y satisfy the equation

$\displaystyle \arcsin 2x+\arcsin y+\arcsin (xy)=0$

find $\displaystyle \frac{dy}{dx}$ when x=y=0

I have done the first part, proving $\displaystyle \frac{d}{dx} \arcsin x=\frac{1}{\sqrt{1-x^2}}$.

I don't know how to do this second part. Differentiating arcsinx I know how, but arcsiny and arcsin(xy) I don't know what to do. Any pointers?

Thanks