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?