Derivative of ln(1-3x)

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

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(1 - 3 x\right)$:

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

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

         So, the result is: $-3$

      The result is: $-3$

   The result of the chain rule is:

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

4. Now simplify:

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

The answer is: