Let \( f(x)=\left\{\begin{array}{c}g(x) \cdot \cos \frac{1}{x}, x \neq 0 \\ 0, \quad x=0\end{arr...

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Let \( f(x)=\left\{\begin{array}{c}g(x) \cdot \cos \frac{1}{x}, x \neq 0 \\ 0, \quad x=0\end{array}\right. \) where \( g(x) \) is an even function differentiable at \( x=0 \), passing through the origin. Then \( f^{\prime}(0) \)
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