Derivative of 6x-4-(6/x^4)

1. Differentiate $\left(6 x - 4\right) - \frac{6}{x^{4}}$ term by term:

   1. Differentiate $6 x - 4$ term by term:

      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: $6$

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

      The result is: $6$

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

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

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

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

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

         The result of the chain rule is:

         $$- \frac{4}{x^{5}}$$

      So, the result is: $\frac{24}{x^{5}}$

   The result is: $6 + \frac{24}{x^{5}}$

The answer is:

$$6 + \frac{24}{x^{5}}$$