Derivative of f(x)=(2x+1)(3x-2)

1. Apply the product rule:

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

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

   $g{\left(x \right)} = 3 x - 2$; to find $\frac{d}{d x} g{\left(x \right)}$:

   1. Differentiate $3 x - 2$ 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: $3$

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

      The result is: $3$

   The result is: $12 x - 1$

The answer is:

$$12 x - 1$$