Derivative of x^2*(x+4)

1. Apply the product rule:

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

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

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

   $g{\left(x \right)} = x + 4$; 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: $x^{2} + 2 x \left(x + 4\right)$

2. Now simplify:

   $$x \left(3 x + 8\right)$$

The answer is:

$$x \left(3 x + 8\right)$$