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

Feb 15, 2017

$\frac{d}{\mathrm{dx}} \frac{2}{x + 1} ^ 2 = - \frac{4}{x + 1} ^ 3$

#### Explanation:

$f \left(x\right) = \frac{2}{x + 1} ^ 2 = 2 {\left(x + 1\right)}^{- 2}$

We can differentiate using the power rule and the chain rule:

$\frac{d}{\mathrm{dx}} \frac{2}{x + 1} ^ 2 = \frac{d}{\mathrm{dx}} 2 {\left(x + 1\right)}^{- 2} = 2 \left(- 2\right) {\left(x + 1\right)}^{- 3} \frac{d}{\mathrm{dx}} \left(x + 1\right) = - \frac{4}{x + 1} ^ 3$