#### Answer

\[y' = \frac{{2\sqrt y }}{{1 - 4\sqrt y }}\]

#### Work Step by Step

\[find\,\,\frac{{dy}}{{dx}}\,\,\,\,using\,\,implicit\,\,\,differentitation.\]
\[1 + 2y' = \frac{1}{{2\sqrt y }} \cdot y'\]
\[then\]
\[2y' - \frac{{y'}}{{2\sqrt y }} = - 1\]
\[factor\,\,out\,\,y'\]
\[\begin{gathered}
y'\,\left( {2 - \frac{1}{{2\sqrt y }}} \right) = - 1 \hfill \\
\hfill \\
y' = - \frac{1}{{2 - \frac{1}{{2\sqrt y }}}} \hfill \\
\hfill \\
\end{gathered} \]
\[\begin{gathered}
simplify \hfill \\
\hfill \\
y' = \frac{{2\sqrt y }}{{1 - 4\sqrt y }} \hfill \\
\end{gathered} \]