Logarithmic Differentiation Process

I.

For $y(x)=\frac{(x^2+1)^3}{\sqrt{x-1}}$ (with x > 1), taking natural logarithms gives $\ln(y)=3\ln(x^2+1)-\frac{1}{2}\ln(x-1)$.

II.

Differentiating both sides yields $\frac{y'}{y}= \frac{6*x}{x^2+1}-\frac{1}{2*(x-1)}$.

III.

Thus, the derivative is given by $y'= y*\left(\frac{6*x}{x^2+1}+\frac{1}{2*(x-1)}\right)$.

Which of the above statements regarding logarithmic differentiation are true?