Answer
$$ \begin{aligned}
f(x) & = \, x \, \\[2 em]
f\prime(x) &= {{10000\,a^3\,x^4-24000\,a^3\,x^2+5000\,a^6+14400\,a^3}\over{\left( 25\,x^4-60\,x^2+50\,a^3+36\right)^2}}
\end{aligned} $$
Explanation
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