Derivative of y=x+5x^-4+1

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

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

      1. Apply the power rule: $x$ goes to $1$

      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: $1 - \frac{20}{x^{5}}$

   2. The derivative of the constant $1$ is zero.

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

The answer is:

$$1 - \frac{20}{x^{5}}$$