Derivative of sqrt(x-36)

1. Let $u = x - 36$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 36\right)$:

   1. Differentiate $x - 36$ term by term:

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

      2. The derivative of the constant $-36$ is zero.

      The result is: $1$

   The result of the chain rule is:

   $$\frac{1}{2 \sqrt{x - 36}}$$

4. Now simplify:

   $$\frac{1}{2 \sqrt{x - 36}}$$

The answer is:

$$\frac{1}{2 \sqrt{x - 36}}$$