$$\displaystyle\frac{d}{d x } \left( \frac{ 1 }{ ( \sqrt{ x } - \frac{ 1 }{ x } +1) } \right)$$
$\frac{-x^{\frac{3}{2}}-2}{2\left(x^{\frac{3}{2}}+x-1\right)^{2}}$
$x\geq 0$
$\frac{3x^{2}+x^{\frac{3}{2}}+15\sqrt{x}+8}{4\left(x^{\frac{3}{2}}+x-1\right)^{3}}$
$x\geq 0$
