\[ y = {2 \over x} = 2\cdot {1 \over x} = 2\cdot x^{-1} \]
\[ y\,' = (-1) \cdot 2 \cdot x^{-1-1} = -2 \cdot x^{-2} = -2\cdot \left({1 \over x^2}\right) = -{2 \over x^2} \]