Prove that the derivative of \( \tan ^{-1} \frac{\sqrt{1+x^{2}}-1}{...

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Prove that the derivative of \( \tan ^{-1} \frac{\sqrt{1+x^{2}}-1}{x} \) w.r.t. \( \tan ^{-1} x \) is independent of \( x \).
\( \mathrm{P} \)
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