Calculus (3rd Edition)

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