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

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. Differentiate $x - 2$ term by term:

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

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

      The result is: $1$

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

   1. Differentiate $x - 3$ term by term:

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

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

      The result is: $1$

   The result is: $2 x - 5$

The answer is:

$$2 x - 5$$