Derivative of (6x³-3)(x+4)

1. Apply the product rule:

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

   $f{\left(x \right)} = 6 x^{3} - 3$; to find $\frac{d}{d x} f{\left(x \right)}$:

   1. Differentiate $6 x^{3} - 3$ 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: $18 x^{2}$

      2. The derivative of the constant $\left(-1\right) 3$ is zero.

      The result is: $18 x^{2}$

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

   1. Differentiate $x + 4$ term by term:

      1. Apply the power rule: $x$ goes to $1$

      2. The derivative of the constant $4$ is zero.

      The result is: $1$

   The result is: $6 x^{3} + 18 x^{2} \left(x + 4\right) - 3$

2. Now simplify:

   $$24 x^{3} + 72 x^{2} - 3$$

The answer is:

$$24 x^{3} + 72 x^{2} - 3$$