Đáp án:
$\begin{array}{l}
y = \frac{x}{a} + \frac{b}{{{x^2}}} + c\sqrt x + \frac{{{a^2}}}{2} + \sqrt[3]{b}\\
y = \frac{1}{a}.x + b.{x^{ - 2}} + c.{x^{\frac{1}{2}}} + \frac{{{a^2}}}{2} + \sqrt[3]{b}\\
\Rightarrow y' = \frac{1}{a} + b.\left( { - 2} \right).{x^{ - 2 - 1}} + c.\frac{1}{2}.{x^{\frac{1}{2} - 1}} + \frac{{{a^2}}}{2} + \sqrt[3]{b}\\
y' = \frac{1}{a} - \frac{{2b}}{{{x^3}}} + \frac{{c.{x^{ - \frac{1}{2}}}}}{2} + \frac{{{a^2}}}{2} + \sqrt[3]{b}\\
y' = - \frac{{2b}}{{{x^3}}} + \frac{c}{{2\sqrt x }} + \frac{1}{a} + \frac{{{a^2}}}{2} + \sqrt[3]{b}
\end{array}$