Let \( f \) be a differentiable function satisfying the condition \( f\left(\frac{x}{y}\right)=\....

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Let \( f \) be a differentiable function satisfying the condition \( f\left(\frac{x}{y}\right)=\frac{f(x)}{f(y)}(y \neq 0, f(y) \neq 0) \forall x, y \in R \)
\( \mathrm{P} \)
and \( f^{\prime}(1)=2 \). If the smaller area enclosed by \( y=f(x) \), \( x^{2}+y^{2}=2 \) is \( A \), then find [A], where [.] represents the greatest integer function.


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