$\displaystyle \begin{array}{{>{\displaystyle}l}} 1.\ y=\left(\sqrt{x} -\frac{1}{\sqrt{x}}\right)^{2} =x+\frac{1}{x} -2\\ \Rightarrow y'=1-\frac{1}{x^{2}}\\ 2.\ y=\sqrt{x^{2} +1} -\sqrt{1-x^{2}}\\ y'=\frac{\left( x^{2} +1\right) '}{2\sqrt{x^{2} +1}} -\frac{\left( 1-x^{2}\right) '}{2\sqrt{1-x^{2}}} =\frac{2x}{2\sqrt{x^{2} +1}} +\frac{2x}{2\sqrt{1-x^{2}}}\\ \end{array}$