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That derivative is - 1 / (x + 1)²
[latex]y=\frac{1}{x+1}+2=(x+1)^{-1}+2\\\\y'=\left[(x+1)^{-1}+2\right]'=-(x+1)^{-1-1}=-(x+1)^{-2}=-\frac{1}{(x+1)^2}[/latex]
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That derivative is - 1 / (x + 1)²
[latex]y=\frac{1}{x+1}+2=(x+1)^{-1}+2\\\\y'=\left[(x+1)^{-1}+2\right]'=-(x+1)^{-1-1}=-(x+1)^{-2}=-\frac{1}{(x+1)^2}[/latex]