Derivative of x/5+5/x

1. Differentiate $\frac{x}{5} + \frac{5}{x}$ 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: $\frac{1}{5}$

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

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

      So, the result is: $- \frac{5}{x^{2}}$

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

The answer is:

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