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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