Derivative of (3*sqrt(3))/(2*x)

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

   1. Let $u = 2 x$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$:

      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: $2$

      The result of the chain rule is:

      $$- \frac{1}{2 x^{2}}$$

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

The answer is:

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