Derivative of y=ln3x^2

1. Let $u = \log{\left(3 x \right)}$.

2. Apply the power rule: $u^{2}$ goes to $2 u$

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

   1. Let $u = 3 x$.

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

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

      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: $3$

      The result of the chain rule is:

      $$\frac{1}{x}$$

   The result of the chain rule is:

   $$\frac{2 \log{\left(3 x \right)}}{x}$$

The answer is:

$$\frac{2 \log{\left(3 x \right)}}{x}$$