Derivative of (3x^2-2)^2

1. Let $u = 3 x^{2} - 2$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x^{2} - 2\right)$:

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

         So, the result is: $6 x$

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

      The result is: $6 x$

   The result of the chain rule is:

   $$6 x \left(6 x^{2} - 4\right)$$

4. Now simplify:

   $$36 x^{3} - 24 x$$

The answer is:

$$36 x^{3} - 24 x$$