$$ \begin{aligned} f(x) & = \, x \, \\[2 em] f\prime(x) &= {{\sqrt{x}\,\left(24\,e\,x^3\,{\it sqrt}+\left(24\,x^3-36\,x^5 \right)\,e^{3\,x^2}\right)-e\,\ln \,{\it sqrt}+\left(12\,x^2-1 \right)\,e^{3\,x^2}\,\ln }\over{2\,\sqrt{x}\,\left(e\,{\it sqrt}+e ^{3\,x^2}\right)^2}} \end{aligned} $$

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