导数 log(x-3)

1. Let $u = x - 3$.

2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$.

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 3\right)$:

   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 of the chain rule is:

   $$\frac{1}{x - 3}$$

4. Now simplify:

   $$\frac{1}{x - 3}$$

The answer is:

$$\frac{1}{x - 3}$$