Derivative of (x-3)(log2)(x-3)

1. Apply the product rule:

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

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

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

      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: $1$

      So, the result is: $\log{\left(2 \right)}$

   $g{\left(x \right)} = x - 3$; 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: $2 \left(x - 3\right) \log{\left(2 \right)}$

2. Now simplify:

   $$2 \left(x - 3\right) \log{\left(2 \right)}$$

The answer is:

$$2 \left(x - 3\right) \log{\left(2 \right)}$$