Derivative of 64*sqrt(3)/((5*x^5))

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

   1. Let $u = 5 x^{5}$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x^{5}$:

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

         1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$

         So, the result is: $25 x^{4}$

      The result of the chain rule is:

      $$- \frac{1}{x^{6}}$$

   So, the result is: $- \frac{64 \sqrt{3}}{x^{6}}$

The answer is:

$$- \frac{64 \sqrt{3}}{x^{6}}$$