Derivative of (2x^2+4)(4x-2)

1. Apply the product rule:

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

   $f{\left(x \right)} = 2 x^{2} + 4$; to find $\frac{d}{d x} f{\left(x \right)}$:

   1. Differentiate $2 x^{2} + 4$ 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: $4 x$

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

      The result is: $4 x$

   $g{\left(x \right)} = 4 x - 2$; to find $\frac{d}{d x} g{\left(x \right)}$:

   1. Differentiate $4 x - 2$ 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: $x$ goes to $1$

         So, the result is: $4$

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

      The result is: $4$

   The result is: $8 x^{2} + 4 x \left(4 x - 2\right) + 16$

2. Now simplify:

   $$24 x^{2} - 8 x + 16$$

The answer is: