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Calculus Level 3

Let \( f(x) = \frac{1}{2} \left[ f(xy) + f( \frac{x}{y} ) \right] \) for \( x, y \in \mathbb{R}^+ \), and satisfy the condition that \( f(1) = 0\) and \( f'(1) = 2 \).

Find the value of \(f'(3) \).

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