Answer
inside: $g(x)=72e^{0.6x}$
outside: $f(g)=72e^{g}$
derivative: $f^{\prime}(x)=43.2e^{0.6x}$
Work Step by Step
Given$$
f(x)=72e^{0.6 x}
$$
Use the chain rule to take the derivative
$$
\frac{d f(g(x))}{d x}=f^{\prime}(g(x)) g^{\prime}(x)
$$
Here $g(x)=0.6x$ and $f(g)=72e^g,$ then
\begin{align*}
f^{\prime}(x) &=\left(72e^{g(x)}\right)^{\prime} \\
&=72e^{g(x)} g^{\prime}(x) \\
&=(72)(0.6)e^{0.6x} \\
&=43.2e^{0.6x}
\end{align*}
