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Let f:(0,oo)to(0,oo) be a differentiable...

Let `f:(0,oo)to(0,oo)` be a differentiable function satisfying, `int_0^x(1-t)f(t)dt=int_0^x tf(t)dt` ; `x in R^+` and `f(1)=1.` Determine `f(x)dot`

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