Derivative of sin(3-x)

1. Let $u = 3 - x$.

2. The derivative of sine is cosine:

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

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

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

      1. The derivative of the constant $3$ 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: $-1$

   The result of the chain rule is:

   $$- \cos{\left(x - 3 \right)}$$

The answer is:

$$- \cos{\left(x - 3 \right)}$$