A calculus problem by Archit Tripathi

Calculus Level 5

If \(f\) is a differentiable function [other than \((f(x) = x)\)] which satisfies:

\(f(x+f(y)+xf(y)) = y+f(x)+yf(x)\) for all real \(x, \ y \ne -1\), then find the value of \(4034[1+f(2016)].\)

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