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Consider the function f(x)=x1+x1+x1+⋱.\displaystyle f(x) = \frac{x}{1+\frac{x}{1+\frac{x}{1+\ddots}}}. f(x)=1+1+1+⋱xxx.
Determine the value of f′(0). f'(0).f′(0).
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