Derivative of 2x³-1/x²

1. Differentiate $2 x^{3} - 1 \cdot \frac{1}{x^{2}}$ 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: $x^{3}$ goes to $3 x^{2}$

      So, the result is: $6 x^{2}$

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

      1. Let $u = x^{2}$.

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

      3. 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:

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

      So, the result is: $\frac{2}{x^{3}}$

   The result is: $6 x^{2} + \frac{2}{x^{3}}$

2. Now simplify:

   $$\frac{2 \cdot \left(3 x^{5} + 1\right)}{x^{3}}$$

The answer is:

$$\frac{2 \cdot \left(3 x^{5} + 1\right)}{x^{3}}$$