Derivative of ln(2y)/2

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

   1. Let $u = 2 y$.

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

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

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

         1. Apply the power rule: $y$ goes to $1$

         So, the result is: $2$

      The result of the chain rule is:

      $$\frac{1}{y}$$

   So, the result is: $\frac{1}{2 y}$

The answer is:

$$\frac{1}{2 y}$$