Okay, here we have this:
We need to find the derivative of the following function:
[tex]\begin{gathered} f(x)=x^{3}\: -\: 1/x^{2}\: +\: 2\: \sqrt{x}\: -3/x \\ y=x^{3}\: -\: 1/x^{2}\: +\: 2\: \sqrt{x}\: -3/x \end{gathered}[/tex]
We obtain the following:
[tex]\begin{gathered} \frac{d}{dx}\mleft(y\mright)=\frac{d}{dx}\mleft(x^3-\frac{1}{x^2}+2\sqrt{x}-\frac{3}{x}\mright) \\ =\frac{d}{dx}\mleft(x^3\mright)-\frac{d}{dx}\mleft(\frac{1}{x^2}\mright)+\frac{d}{dx}\mleft(2\sqrt{x}\mright)-\frac{d}{dx}\mleft(\frac{3}{x}\mright) \\ =3x^2-\mleft(-\frac{2}{x^3}\mright)+\frac{1}{\sqrt{x}}-\mleft(-\frac{3}{x^2}\mright) \\ \frac{dy}{dx}=3x^2+\frac{2}{x^3}+\frac{1}{\sqrt{x}}+\frac{3}{x^2} \end{gathered}[/tex]
