Function got a little lengthy for sake of symmetry!

Calculus Level 3

If provided s+e+a=0s+e+a=0 and a function ff is defined as f(c)=1cs+ce+1+1ce+ca+1+1ca+cs+1.\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)f(c) at c=πc=\pi.

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