Derivative of sqrt(5-x)

1. Let $u = 5 - x$.

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

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

   1. Differentiate $5 - x$ term by term:

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

      2. The derivative of a constant times a function is the constant times the derivative of the function.

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

         So, the result is: $-1$

      The result is: $-1$

   The result of the chain rule is:

   $$- \frac{1}{2 \sqrt{5 - x}}$$

The answer is:

$$- \frac{1}{2 \sqrt{5 - x}}$$