Find the sub-intervals in which f ( x )= log (2+ x )-x/(2+ x), x >-2 is increasing or decreasing.

$$\mathrm{f}^{\prime}(\mathrm{x})=\frac{1}{2+\mathrm{x}}-\frac{2}{(2+\mathrm{x})^{2}}=\frac{\mathrm{x}}{(2+\mathrm{x})^{2}} $$ Sign of $\displaystyle \mathrm{f}^{\prime}(\mathrm{x})$ $\displaystyle \mathrm{f}(\mathrm{x})$ is decreasing in ( $\displaystyle -2,0$ ) and increasing in ( $\displaystyle 0, \infty$ )