Derivative of 0,5ln²(x)

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

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

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

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

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

      The result of the chain rule is:

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

   So, the result is: $\frac{\log{\left(x \right)}}{x}$

The answer is:

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