Derivative of cos(5-3*x)

1. Let $u = 5 - 3 x$.

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 $\frac{d}{d x} \left(5 - 3 x\right)$:

   1. Differentiate $5 - 3 x$ term by term:

      1. The derivative of the constant $5$ 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: $-3$

      The result is: $-3$

   The result of the chain rule is:

   $$- 3 \sin{\left(3 x - 5 \right)}$$

The answer is:

$$- 3 \sin{\left(3 x - 5 \right)}$$