Answer
\[\frac{{dy}}{{dx}} = 30\,{\left( {3x + 7} \right)^9}\]
Work Step by Step
\[\begin{gathered}
y = \,{\left( {3x + 7} \right)^{10}} \hfill \\
\hfill \\
Use\,\,the\,\,version\,\,1\,\,of\,\,the\,\,chain\,\,rule \hfill \\
\hfill \\
{\text{ }}\frac{{dy}}{{dx}} = \frac{{dy}}{{du}} \cdot \frac{{du}}{{dx}} \hfill \\
\hfill \\
set{\text{ }}u = 3x + 7 \hfill \\
\hfill \\
then \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = 10\,{\left( {3x + 7} \right)^{10 - 1}}\,{\left( {3x + 7} \right)^,} \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = 10\,{\left( {3x + 7} \right)^9}\,\left( 3 \right) \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = 30\,{\left( {3x + 7} \right)^9} \hfill \\
\end{gathered} \]
