Answer
inside: $g(x)=3.7x$
outside: $f(g)=e^{g}$
derivative: $f^{\prime}(x)=3.7e^{3.7x}$
Work Step by Step
Given$$
f(x)=e^{3.7 x}
$$
Use the chain rule to take the derivative
$$
\frac{d f(g(x))}{d x}=f^{\prime}(g(x)) g^{\prime}(x)
$$
Here $g(x)=3.7x$ and $f(g)=e^g,$ then
\begin{align*}
f^{\prime}(x) &=\left(e^{g(x)}\right)^{\prime} \\
&=e^{g(x)} g^{\prime}(x) \\
&=3.7e^{3.7x}
\end{align*}
