Derivative of y=(lnx-1)^2

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

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

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

   1. Differentiate $\log{\left(x \right)} - 1$ term by term:

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

      2. The derivative of the constant $-1$ is zero.

      The result is: $\frac{1}{x}$

   The result of the chain rule is:

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

4. Now simplify:

   $$\frac{2 \left(\log{\left(x \right)} - 1\right)}{x}$$

The answer is:

$$\frac{2 \left(\log{\left(x \right)} - 1\right)}{x}$$