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Black Book Advanced Problems in MathematicsMathematicsContinuity and Differentiability

Let f : R^+ R be a differentiable function satisfying : f(xy) = f(x) y + f(y) x x, y R^+ also f(1) = 0; f'(1) = 1 find _ x e [ 1 f(x) ] (where [ ] denotes greatest integer function).

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