Derivative of 1/(8x^4)

1. Let $u = 8 x^{4}$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 8 x^{4}$:

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

      1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$

      So, the result is: $32 x^{3}$

   The result of the chain rule is:

   $$- \frac{1}{2 x^{5}}$$

The answer is:

$$- \frac{1}{2 x^{5}}$$