Verified answer

[tex]\displaystyle\bf\\y=x^{2}-\frac{1}{x}=x^{2}-x^{-1} \\\\\\y'=(x^{2} )'-(x^{-1} )'=2x-(-1\cdot x^{-2})=2x+x^{-2} =2x+\frac{1}{x^{2} }[/tex]