Derivative of ln(5-2x)

1. Let $u = 5 - 2 x$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(5 - 2 x\right)$:

   1. Differentiate $5 - 2 x$ 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. 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: $2$

         So, the result is: $-2$

      The result is: $-2$

   The result of the chain rule is:

   $$- \frac{2}{5 - 2 x}$$

4. Now simplify:

   $$\frac{2}{2 x - 5}$$

The answer is:

$$\frac{2}{2 x - 5}$$