<s>[INST] Using logarithmic differentiation or otherwise, differentiate $y = (x −1) (x − 2) (x − 3$)? And show that $y' = 3x^2-12x+11$ So far this is my method:
\begin{align*}
y = (x-1)(x-2)(x-3) & \Longleftrightarrow \ln(y) = \ln(x-1) + \ln(x-2) + \ln(x-3)\\\\
& \Longleftrightarrow \frac{y'}{y} = \frac{1}{x-1} + \frac{1}{x-2} + \frac{1}{x-3}\\\\
& \Longleftrightarrow 
y' = y\left(\frac{1}{x-1} + \frac{1}{x-2} + \frac{1}{x-3}\right)
\end{align*}
 [/INST] You are almost done.
Recall $y = (x-1)(x-2)(x-3)$.
So $y{'} = (x-1)(x-2)(x-3)(\frac{1}{x-1}+\frac{1}{x-2}+\frac{1}{x-3}) = (x-2)(x-3)+(x-1)(x-3)+(x-1)(x-2) = 3x^2-12x+11.$
</s>