Derivative of (-3+x³)(-4x³+3)

1. Apply the product rule:

   $$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$$

   $f{\left(x \right)} = x^{3} - 3$; to find $\frac{d}{d x} f{\left(x \right)}$:

   1. Differentiate $x^{3} - 3$ term by term:

      1. The derivative of the constant $-3$ is zero.

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

      The result is: $3 x^{2}$

   $g{\left(x \right)} = 3 - 4 x^{3}$; to find $\frac{d}{d x} g{\left(x \right)}$:

   1. Differentiate $3 - 4 x^{3}$ 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: $x^{3}$ goes to $3 x^{2}$

         So, the result is: $- 12 x^{2}$

      2. The derivative of the constant $3$ is zero.

      The result is: $- 12 x^{2}$

   The result is: $3 x^{2} \cdot \left(3 - 4 x^{3}\right) - 12 x^{2} \left(x^{3} - 3\right)$

2. Now simplify:

   $$x^{2} \cdot \left(45 - 24 x^{3}\right)$$

The answer is:

$$x^{2} \cdot \left(45 - 24 x^{3}\right)$$