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Problem:
\(If \ f(x) \ satisfies \ the \ relation: f(x+y) = y\frac{|x-1|}{(x-1)}f(x) + f(y) \ with \ f(1) = 2, \ then \ what \ is \ \lim_{x\to1} f'(x)? \)

I found f(x) = 2(1 + |-x|) / (1 - |x-x^2|). I can't differentiate this function. Whhat to do?

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