Derivative of y=-sqrt3x+4

1. Differentiate $4 - \sqrt{3 x}$ term by term:

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

      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:

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

      So, the result is: $- \frac{\sqrt{3}}{2 \sqrt{x}}$

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

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

The answer is:

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