# How do you differentiate y = (x) / (x+1)?

We can use the quotient rule, which states that for $y = f \frac{x}{g} \left(x\right)$, $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{f ' \left(x\right) g \left(x\right) - f \left(x\right) g ' \left(x\right)}{g} {\left(x\right)}^{2}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\left(1\right) \left(x + 1\right) - \left(x\right) \left(1\right)}{x + 1} ^ 2 = \frac{x + 1 - x}{x + 1} ^ 2 = \frac{1}{x + 1} ^ 2 = {\left(x + 1\right)}^{- 2}$