解答

$${y=\frac{x}{\sqrt{x-1}}}$$

$$\begin{eqnarray*} y'&=& \frac{x'\sqrt{x-1}-x(\sqrt{x-1})'}{(\sqrt{x-1})^2}\\ ... ...(x-1)-x}{2(x-1)\sqrt{x-1}}\\ &=& \frac{x-2}{2(x-1)\sqrt{x-1}} \end{eqnarray*}$$