Derivative of ln(2x^3)

1. Let $u = 2 x^{3}$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x^{3}$:

   1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$

      So, the result is: $6 x^{2}$

   The result of the chain rule is:

   $$\frac{3}{x}$$

The answer is:

$$\frac{3}{x}$$