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If provided $s+e+a=0$ and a function $f$ is defined as $\large f(c)=\dfrac{1}{c^s +c^{-e}+1}+\dfrac{1}{c^e +c^{-a}+1}+\dfrac{1}{c^a +c^{-s}+1} .$

Find the derivative of $f(c)$ at $c=\pi$.

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