Answer
$$\frac{-x}{(x+2)^2\sqrt{x+1}}.$$
Work Step by Step
Since $ y=\frac{(x+1)^{1/2}}{x+2}$, then we can rewrite it as follows
$$ y=(x+1)^{1/2} (x+2)^{-1}.$$
Now, by using the product rule, the derivative $ y'$ is given by
$$ y'=\frac{1}{2}(x+1)^{-1/2} (x+2)^{-1}-(x+1)^{1/2} (x+2)^{-2}\\
=\frac{1}{2(x+2)\sqrt{x+1}}-\frac{\sqrt{x+1}}{(x+2)^2}\\
=\frac{x+2-2(x+1)}{(x+2)^2\sqrt{x+1}}=\frac{-x}{(x+2)^2\sqrt{x+1}}.$$
