#### Answer

\[ = \frac{{\cos \frac{x}{4}}}{4}\]

#### Work Step by Step

\[\begin{gathered}
y = \sin \frac{x}{4} \hfill \\
\hfill \\
y = f\,\left( u \right) = \sin u \hfill \\
\hfill \\
set\,\,u = g\,\left( x \right) = \frac{x}{4} \hfill \\
\hfill \\
Use\,\,the\,\,version\,\,1\,\,of\,\,the\,\,chain\,\,rule \hfill \\
\hfill \\
{\text{ }}\frac{{dy}}{{dx}} = \frac{{dy}}{{du}} \cdot \frac{{du}}{{dx}} \hfill \\
\hfill \\
Therefore \hfill \\
\hfill \\
\,\frac{{dy}}{{dx}} = \frac{d}{{du}}\,\left( {\sin u} \right) \cdot \frac{d}{{dx}}\,\left( {\frac{x}{4}} \right) \hfill \\
\hfill \\
then \hfill \\
\hfill \\
= \cos u \cdot \frac{1}{4} \hfill \\
\hfill \\
= \frac{{\cos \frac{x}{4}}}{4} \hfill \\
\hfill \\
\end{gathered} \]