If \( f(x)=\tan ^{-1} x, g(x)=\tan ^{-1}\left(\frac{1+x}{1-x}\right...

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If \( f(x)=\tan ^{-1} x, g(x)=\tan ^{-1}\left(\frac{1+x}{1-x}\right) \) for \( |x|1 \), show that \( f^{\prime}(x)=g^{\prime}(x) \) and \( g(x)-f(x)=\frac{\pi}{4} \).
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