## Calculus (3rd Edition)

$$\frac{-x}{(x+2)^2\sqrt{x+1}}.$$
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 $$y'=\frac{1}{2}(x+1)^{-1/2} (x+2)^{-1}-(x+1)^{1/2} (x+2)^{-2}\\ =\frac{1}{2(x+2)\sqrt{x+1}}-\frac{\sqrt{x+1}}{(x+2)^2}\\ =\frac{x+2-2(x+1)}{(x+2)^2\sqrt{x+1}}=\frac{-x}{(x+2)^2\sqrt{x+1}}.$$