\(y = \frac{x}{x + 1}\)

Using quotient rule because the function is of the form \(\frac{u(x)}{v(x)}\)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{v\frac{\mathrm d u}{\mathrm d x} - u\frac{\mathrm d v}{\mathrm d x}}{v^{2}}\)

\(\frac{\mathrm d y}{\mathrm d x} = \frac{(x + 1) . 1 - x . 1}{(x + 1)^{2}}\)

= \(\frac{1}{(x + 1)^{2}}\)