\begin{question}
What is the derivative of $f(x) = x^{7} e^{0.2 x}$, evaluated at $x = 0.9$?
\end{question}

\begin{solution}
Using the product rule we obtain
\[ f'(x) = e^{0.2 x} \cdot (7 \cdot x^6 + 0.2 \cdot x^7). \]
Evaluated at $x = 0.9$ and rounded to two digits the answer is
$f'(0.9) = 4.568278 \approx 4.57$.
\end{solution}

\extype{num}
\exsolution{4.57}
\exname{exp derivative}
\extol{0.01}