Answer
$\frac{3}{2}\sqrt x-\frac{1}{2\sqrt x}-\frac{1}{\sqrt {x^{3}}}$
Work Step by Step
Start with the function $y=\frac{x^{2}-x+2}{x^{1/2}}$.
Divide each term of the fraction: $y=x^{3/2}-x^{1/2}+2x^{-1/2}$.
Differentiate using the power rule for each term: $y'=\frac{3}{2}x^{1/2}-\frac{1}{2}x^{-1/2}-x^{-3/2}$.
Change from fractional power form to radical form to arrive at the answer:
$\frac{3}{2}\sqrt x-\frac{1}{2\sqrt x}-\frac{1}{\sqrt {x^{3}}}$.
