If \( x=\log \left(1+t^{2}\right) \) and \( y=t-\tan ^{-1} t \). Th...

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If \( x=\log \left(1+t^{2}\right) \) and \( y=t-\tan ^{-1} t \). Then, \( \frac{d y}{d x} \) is
\( \mathrm{P} \)
W equal to
(A) \( e^{x}-1 \)
(B) \( t^{2}-1 \)
(C) \( \frac{\sqrt{e^{x}-1}}{2} \)
(D) \( e^{x}-y \)
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