Derivative of 3*x^2-1/x^3

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

      So, the result is: $6 x$

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

      1. Let $u = x^{3}$.

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

      3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{3}$:

         1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

         The result of the chain rule is:

         $$- \frac{3}{x^{4}}$$

      So, the result is: $\frac{3}{x^{4}}$

   The result is: $6 x + \frac{3}{x^{4}}$

The answer is:

$$6 x + \frac{3}{x^{4}}$$