## Calculus (3rd Edition)

$$y''=-\frac{1}{4}r^{-3/2}-\frac{3}{4}r^{-1/2}-2, \quad y'''=\frac{3}{8}r^{-5/2}+\frac{3}{8}r^{-3/2}.$$
Let $y=(r^{1/2}+r)(1-r)$; simplify $y$ as follows $$y=r^{1/2}+r-r^{3/2}-r^2.$$ Now, we get $$y'=\frac{1}{2}r^{-1/2}+1-\frac{3}{2}r^{1/2}-2r.$$ $$y''=-\frac{1}{4}r^{-3/2}-\frac{3}{4}r^{-1/2}-2, \quad y'''=\frac{3}{8}r^{-5/2}+\frac{3}{8}r^{-3/2}.$$