$f(x)=\Bigg(\sqrt{x}-\dfrac{1}{\sqrt{x}}\Bigg)^2\\\to f'(x)=\Bigg[\Bigg(\sqrt{x}-\dfrac{1}{\sqrt{x}}\Bigg)^2\Bigg]'\\=2\Bigg(\sqrt{x}-\dfrac{1}{\sqrt{x}}\Bigg).\Bigg(\sqrt{x}-\dfrac{1}{\sqrt{x}}\Bigg)'\\=2\Bigg(\sqrt{x}-\dfrac{1}{\sqrt{x}}\Bigg).\Bigg(\dfrac{1}{2\sqrt{x}}+\dfrac{1}{2x\sqrt{x}}\Bigg)\\=2.\dfrac{x-1}{\sqrt{x}}.\dfrac{x+1}{2x\sqrt{x}}\\=\dfrac{x^2-1}{x^2}$
