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Let f : R^(+) rarr R satisfies the funct...

Let `f : R^(+) rarr R` satisfies the functional equation `f(xy) = e^(xy - x - y) {e^(y) f(x) + e^(x) f(y)}, AA x, y in R^(+)`. If f'(1) = e, determine f(x).

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The correct Answer is:
`f(x)=e^(x)logx`
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