Derivative of 1/(x+1)^2

1. Let $u = \left(x + 1\right)^{2}$.

2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 1\right)^{2}$:

   1. Let $u = x + 1$.

   2. Apply the power rule: $u^{2}$ goes to $2 u$

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 1\right)$:

      1. Differentiate $x + 1$ term by term:

         1. Apply the power rule: $x$ goes to $1$

         2. The derivative of the constant $1$ is zero.

         The result is: $1$

      The result of the chain rule is:

      $$2 x + 2$$

   The result of the chain rule is:

   $$- \frac{2 x + 2}{\left(x + 1\right)^{4}}$$

4. Now simplify:

   $$\frac{2}{\left(- x - 1\right)^{3}}$$

The answer is: