#### Answer

$$ y'=2x -\frac{3}{2}x^{-5/2} .$$

#### Work Step by Step

Since $ y=\frac{x^4+\sqrt x}{x^2}$, we simplify $ y $ as follows
$$ y=\frac{x^4+\sqrt x}{x^2}= x^2+\frac{\sqrt x}{x^2} =x^2+x^{-3/2}.$$
Recall that $(x^n)'=nx^{n-1}$
Now, the derivative $ y'$ is given by
$$ y'=2x -\frac{3}{2}x^{-5/2} .$$