Derivative of y=sqrt3x+5

1. Differentiate $\sqrt{3 x} + 5$ term by term:

   1. Let $u = 3 x$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 3 x$:

      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: $3$

      The result of the chain rule is:

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

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

   The result is: $\frac{\sqrt{3}}{2 \sqrt{x}}$

The answer is:

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