Derivative of 2/t^3

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

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

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

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

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

      The result of the chain rule is:

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

   So, the result is: $- \frac{6}{t^{4}}$

The answer is:

$$- \frac{6}{t^{4}}$$