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

1. Differentiate $- \left(2 - x\right) \left(2 x + 3\right) + 1$ term by term:

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

   2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the product rule:

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

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

         1. Differentiate $2 - x$ term by term:

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

            2. 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: $-1$

            The result is: $-1$

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

         1. Differentiate $2 x + 3$ 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: $x$ goes to $1$

               So, the result is: $2$

            2. The derivative of the constant $3$ is zero.

            The result is: $2$

         The result is: $1 - 4 x$

      So, the result is: $4 x - 1$

   The result is: $4 x - 1$

The answer is:

$$4 x - 1$$