Answer
\[ = 5{e^{5x - 7}}\]
Work Step by Step
\[\begin{gathered}
y = {e^{5x - 7}} \hfill \\
\hfill \\
y = f\,\left( u \right) = {e^u} \hfill \\
\hfill \\
set\,\,u = g\,\left( x \right) = 5x - 7 \hfill \\
\hfill \\
Use\,\,the\,\,version\,\,1\,\,of\,\,the\,\,chain\,\,rule \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{{dy}}{{du}} \cdot \frac{{du}}{{dx}} \hfill \\
\hfill \\
Therefore \hfill \\
\hfill \\
\frac{{dy}}{{dx}} = \frac{d}{{du}}\,\left( {{e^u}} \right) \cdot \frac{d}{{dx}}\,\left( {5x - 7} \right) \hfill \\
\hfill \\
= {e^u} \cdot 5 \hfill \\
\hfill \\
substitute\,\,\,back\,\,u = 5x - 7 \hfill \\
\hfill \\
= 5{e^{5x - 7}} \hfill \\
\hfill \\
\end{gathered} \]
