Derivative of cos(x-2)

1. Let $u = x - 2$.

2. The derivative of cosine is negative sine:

   $$\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$$

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 2\right)$:

   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: $1$

   The result of the chain rule is:

   $$- \sin{\left(x - 2 \right)}$$

4. Now simplify:

   $$- \sin{\left(x - 2 \right)}$$

The answer is:

$$- \sin{\left(x - 2 \right)}$$