Derivative of 4/x^6

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

   1. Let $u = x^{6}$.

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

   3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{6}$:

      1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$

      The result of the chain rule is:

      $$- \frac{6}{x^{7}}$$

   So, the result is: $- \frac{24}{x^{7}}$

The answer is:

$$- \frac{24}{x^{7}}$$