Derivative of sqrt(x+25)

1. Let $u = x + 25$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 25\right)$:

   1. Differentiate $x + 25$ term by term:

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

      2. The derivative of the constant $25$ is zero.

      The result is: $1$

   The result of the chain rule is:

   $$\frac{1}{2 \sqrt{x + 25}}$$

4. Now simplify:

   $$\frac{1}{2 \sqrt{x + 25}}$$

The answer is:

$$\frac{1}{2 \sqrt{x + 25}}$$