Answer
\[\frac{{dy}}{{dx}} = \frac{{5\sqrt[4]{x}}}{4}\]
Work Step by Step
\[\begin{gathered}
y = {x^{\frac{5}{4}}} \hfill \\
\hfill \\
use\,\,the\,\,Implicit\,\,differentiation \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{5}{4}{x^{\frac{5}{4} - 1}} \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{5}{4}{x^{\frac{1}{4}}} \hfill \\
\hfill \\
{x^{1/4}} = \sqrt[4]{x}\,\,then \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{{5\sqrt[4]{x}}}{4} \hfill \\
\end{gathered} \]
