Let f(x)=eg(x)xf(x) = \frac{e^{g(x)}}{x}f(x)=xeg(x). If g(1)=0g(1) = 0g(1)=0 and g′(1)=2g'(1) = 2g′(1)=2, determine f′(1)f'(1)f′(1).
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