Derivative of sqrt(6-2x)

1. Let $u = 6 - 2 x$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(6 - 2 x\right)$:

   1. Differentiate $6 - 2 x$ term by term:

      1. The derivative of the constant $6$ is zero.

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

         1. 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: $2$

         So, the result is: $-2$

      The result is: $-2$

   The result of the chain rule is:

   $$- \frac{1}{\sqrt{6 - 2 x}}$$

4. Now simplify:

   $$- \frac{\sqrt{2}}{2 \sqrt{3 - x}}$$

The answer is:

$$- \frac{\sqrt{2}}{2 \sqrt{3 - x}}$$