Derivative of 1\x+5x^-4

1. Differentiate $\frac{1}{x} + \frac{5}{x^{4}}$ term by term:

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

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

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

      So, the result is: $- \frac{20}{x^{5}}$

   The result is: $- \frac{1}{x^{2}} - \frac{20}{x^{5}}$

2. Now simplify:

   $$- \frac{x^{3} + 20}{x^{5}}$$

The answer is:

$$- \frac{x^{3} + 20}{x^{5}}$$