We can use the power rule to get the second and third derivative of the function.
[tex]\begin{gathered} \text{First derivative:} \\ y^{\prime}=\mleft(\frac{1}{2}\mright)x^{\frac{1}{2}-1} \\ y^{\prime}=(\frac{1}{2})x^{-\frac{1}{2}} \\ y^{\prime}=\frac{x^{-\frac{1}{2}}}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{Second derivative} \\ y^{\prime}^{\prime}=(-\frac{1}{2})\frac{x^{-\frac{1}{2}-1}}{2} \\ y^{\prime\prime}=-\frac{x^{-\frac{3}{2}}}{4}\text{ or }y^{\prime\prime}=-\frac{1}{4x^{\frac{3}{2}}} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Third derivative} \\ y^{\prime}^{\prime}^{\prime}=(-\frac{3}{2})-\frac{x^{-\frac{3}{2}-1}}{4} \\ y^{\prime\prime\prime}=\frac{3x^{-\frac{5}{2}}}{8}\text{ or }y^{\prime\prime\prime}=\frac{3}{8x^{\frac{5}{2}}} \end{gathered}[/tex]
