Answer
\[\frac{{dy}}{{dx}} = \frac{{10}}{{3\sqrt[3]{{5x + 1}}}}\]
Work Step by Step
\[\begin{gathered}
y = \,{\left( {5x + 1} \right)^{\frac{2}{3}}} \hfill \\
\hfill \\
differentiate \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{2}{3}\,{\left( {5x + 1} \right)^{\frac{2}{3} - 1}}\,\left( 5 \right) \hfill \\
\hfill \\
therefore \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{{10}}{{3\,{{\left( {5x + 1} \right)}^{\frac{1}{3}}}}} \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{{10}}{{3\sqrt[3]{{5x + 1}}}} \hfill \\
\end{gathered} \]
