Derivative of 3x-(sqrt(6x-17))

1. Differentiate $3 x - \sqrt{6 x - 17}$ term by term:

   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: $3$

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

      1. Let $u = 6 x - 17$.

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

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(6 x - 17\right)$:

         1. Differentiate $6 x - 17$ term by term:

            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: $6$

            2. The derivative of the constant $-17$ is zero.

            The result is: $6$

         The result of the chain rule is:

         $$\frac{3}{\sqrt{6 x - 17}}$$

      So, the result is: $- \frac{3}{\sqrt{6 x - 17}}$

   The result is: $3 - \frac{3}{\sqrt{6 x - 17}}$

2. Now simplify:

   $$3 - \frac{3}{\sqrt{6 x - 17}}$$

The answer is:

$$3 - \frac{3}{\sqrt{6 x - 17}}$$