# Play with functions

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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