Use implicit differentiation to find the derivative of $\arcsin(y+x)$

Question

Use implicit differentiation to find the derivative of $\arcsin(y+x)$

I have no idea how to proceed. I now that the derivative of $\arcsin(x)$ is $\frac{1}{\sqrt{1-x^2}}$ but I don't know how to incorporate that into this implicit differentiation problem.

Answer 1

$$\frac{d}{dx}\arcsin(x+y)=\frac{1}{\sqrt{1-(x+y)^2}}\times\frac{d}{dx}(x+y)=\frac{y'+1}{\sqrt{1-(x+y)^2}}$$ It is basically: $$\frac{d}{dx}g(f(x,y(x)))=\frac{dg}{df}\frac{df}{dx}$$