$\begin{array}{l} y = \dfrac{{\sqrt x - 1}}{{\sqrt x + 1}}\\ \Leftrightarrow y' = \dfrac{{\left( {\sqrt x - 1} \right)'\left( {\sqrt x + 1} \right) - \left( {\sqrt x - 1} \right).\left( {\sqrt x + 1} \right)'}}{{{{\left( {\sqrt x + 1} \right)}^2}}}\\ = \dfrac{{\dfrac{1}{{2\sqrt x }}.\left( {\sqrt x + 1} \right) - \left( {\sqrt x - 1} \right).\dfrac{1}{{2\sqrt x }}}}{{{{\left( {\sqrt x + 1} \right)}^2}}}\\ = \dfrac{{\dfrac{1}{2} + \dfrac{1}{{2\sqrt x }} - \dfrac{1}{2} + \dfrac{1}{{2\sqrt x }}}}{{{{\left( {\sqrt x + 1} \right)}^2}}}\\ = \dfrac{{\dfrac{1}{{\sqrt x }}}}{{{{\left( {\sqrt x + 1} \right)}^2}}}\\ = \dfrac{1}{{\sqrt x {{\left( {\sqrt x + 1} \right)}^2}}} \end{array}$
