Derivative of 1/(y+5)

1. Let $u = y + 5$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d y} \left(y + 5\right)$:

   1. Differentiate $y + 5$ term by term:

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

      2. The derivative of the constant $5$ is zero.

      The result is: $1$

   The result of the chain rule is:

   $$- \frac{1}{\left(y + 5\right)^{2}}$$

4. Now simplify:

   $$- \frac{1}{\left(y + 5\right)^{2}}$$

The answer is:

$$- \frac{1}{\left(y + 5\right)^{2}}$$