# How do you find the derivative of 2/(x+1)?

Jun 1, 2015

This expression can be rewritten as $2 {\left(x + 1\right)}^{-} 1$, following the exponential alw that states ${a}^{-} n = \frac{1}{a} ^ n$.

Naming $u = x + 1$, we can rewrite the expression as $y = 2 {u}^{-} 1$ and, thus, derivate it according to the chain rule, which states that

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \frac{\mathrm{du}}{\mathrm{dx}}$

So,

$\frac{\mathrm{dy}}{\mathrm{du}} = - 2 {u}^{-} 2$

$\frac{\mathrm{du}}{\mathrm{dx}} = 1$

Thus

$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(- 2 {u}^{-} 2\right) \left(1\right) = - 2 {\left(x + 1\right)}^{-} 2 = \textcolor{g r e e n}{- \frac{2}{x + 1} ^ 2}$