Answer
\[\frac{{dy}}{{dx}} = - 84{x^2}{\cos ^3}\,\left( {7{x^3}} \right)\,\left( {\sin 7{x^3}} \right)\]
Work Step by Step
\[\begin{gathered}
{\cos ^4}\,\left( {7{x^3}} \right) \hfill \\
\hfill \\
Chain\,\,rule \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = {f^,}\,\left( {g\,\left( t \right)} \right) \cdot {g^,}\,\left( t \right) \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = 4{\cos ^3}\,\left( {7{x^3}} \right)\,\left( { - \sin 7{x^3}} \right)\,{\left( {7{x^3}} \right)^,} \hfill \\
\hfill \\
therefore \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = - 4{\cos ^3}\,\left( {7{x^3}} \right)\,\left( {\sin 7{x^3}} \right)\,\left( {21{x^2}} \right) \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = - 84{x^2}{\cos ^3}\,\left( {7{x^3}} \right)\,\left( {\sin 7{x^3}} \right) \hfill \\
\end{gathered} \]
