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Answer
$$ \begin{aligned}
f(x) & = \, x \, \\[2 em]
f\prime(x) &= {{16\,e^{4\,x-8}}\over{\left(e-1\right)\,\left(e+1\right)\,\left(e^ 2+1\right)\,\left(e^4+1\right)\,\left(e^8+1\right)}}
\end{aligned} $$
Explanation
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