differentiate 1/(x+1) — step-by-step solution

To ease differentiation, the expression

\frac{1}{x + 1}

is turned into

{(x + 1)}^{-1}

Let's perform the differentiation:

{({(x + 1)}^{-1})}^{'}

Apply the differentiation rule:

{(f^{n})}^{'} = n \cdot {(f)}^{'} \cdot f^{(n - 1)}

with f =

x + 1

-1 \cdot {(x + 1)}^{'} \cdot {(x + 1)}^{-2}

- {(x + 1)}^{'} \cdot {(x + 1)}^{-2}

- \frac{{(x + 1)}^{'}}{{(x + 1)}^{2}}

ℹ

(x+1)'

1 + 0

- \frac{1 + 0}{{(x + 1)}^{2}}

▷Result: $- \frac{1}{{(x + 1)}^{2}}$