詳解：等號兩邊同時微分

\(\frac{1}{2}{x^{ - \frac{1}{2}}} + \frac{1}{2}{y^{ - \frac{1}{2}}}y' = 0\) ，整理得 \(\frac{1}{{2\sqrt x }} + \frac{1}{{2\sqrt y }}y' = 0\) ，代入 \((\;9\;,\;4\;)\) ，且令 \(y' = m\)

\(\frac{1}{{2\sqrt 9 }} + \frac{1}{{2\sqrt 4 }}m = 0\quad  \Rightarrow \quad \frac{1}{6} + \frac{m}{4} = 0\quad  \Rightarrow m =  - \frac{2}{3}\quad \)