Derivative of 2*x+1/(x^2)

1. Differentiate $2 x + \frac{1}{x^{2}}$ 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. Let $u = x^{2}$.

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

   4. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$:

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

      The result of the chain rule is:

      $$- \frac{2}{x^{3}}$$

   The result is: $2 - \frac{2}{x^{3}}$

The answer is:

$$2 - \frac{2}{x^{3}}$$