\(y=\left(x-1\right)^{\frac{1}{2}}+\left(x-1\right)^{-\frac{1}{2}}\)
\(\Rightarrow y'=\frac{1}{2}\left(x-1\right)^{-\frac{1}{2}}-\frac{1}{2}\left(x-1\right)^{-\frac{3}{2}}\)
\(\Rightarrow y'=\frac{1}{2\sqrt{x-1}}-\frac{1}{2\sqrt{\left(x-1\right)^3}}\)