Derivative of (2x+1)x+1∧3

1. Differentiate $x \left(2 x + 1\right) + 1$ term by term:

   1. Apply the product rule:

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

      $f{\left(x \right)} = 2 x + 1$; to find $\frac{d}{d x} f{\left(x \right)}$:

      1. Differentiate $2 x + 1$ 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: $2$

         2. The derivative of the constant $1$ is zero.

         The result is: $2$

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

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

      The result is: $4 x + 1$

   2. The derivative of the constant $1$ is zero.

   The result is: $4 x + 1$

The answer is:

$$4 x + 1$$