# How do you differentiate f(x) = 4/(x+1)^2 using the chain rule?

Mar 23, 2016

$f ' \left(x\right) = \frac{- 8}{x + 1} ^ 3$

#### Explanation:

Using the $\textcolor{b l u e}{\text{ chain rule }}$

$\frac{d}{\mathrm{dx}} \left[f \left(g \left(x\right)\right)\right] = f ' \left(g \left(x\right)\right) . g ' \left(x\right)$

Rewrite f(x) $= 4 {\left(x + 1\right)}^{-} 2$

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

$= - 8 {\left(x + 1\right)}^{-} 3 = \frac{- 8}{x + 1} ^ 3$