Derivative of 2x+(2/x)+14

1. Differentiate $\left(2 x + \frac{2}{x}\right) + 14$ term by term:

   1. Differentiate $2 x + \frac{2}{x}$ 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: $2$

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

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

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

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

   2. The derivative of the constant $14$ is zero.

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

The answer is:

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