Differential coefficient of \[\frac{{{\tan }^{-1}}x}{1+{{\tan }^{-1}}x}\] w.r.t. \[{{\tan }^{-1}}x\] is

\[\frac{-1}{2\,{{(1+{{\tan }^{-1}}x)}^{2}}}\]

\[\frac{1}{1+{{\tan }^{-1}}x}\]

\[\frac{-1}{1+{{\tan }^{-1}}x}\]

\[\frac{1}{{{(1+{{\tan }^{-1}}x)}^{^{2}}}}\]

Differential coefficient of \[\frac{{{\tan }^{-1}}x}{1+{{\tan }^{-1}}x

1.	Differential coefficient of \[\frac{{{\tan }^{-1}}x}{1+{{\tan }^{-1}}x}\] w.r.t. \[{{\tan }^{-1}}x\] is
A.	\[\frac{1}{1+{{\tan }^{-1}}x}\]
B.	\[\frac{-1}{1+{{\tan }^{-1}}x}\]
C.	\[\frac{1}{{{(1+{{\tan }^{-1}}x)}^{^{2}}}}\]
D.	\[\frac{-1}{2\,{{(1+{{\tan }^{-1}}x)}^{2}}}\]
Answer» D. \[\frac{-1}{2\,{{(1+{{\tan }^{-1}}x)}^{2}}}\]

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Differential coefficient of \[\frac{{{\tan }^{-1}}x}{1+{{\tan }^{-1}}x}\] w.r.t. \[{{\tan }^{-1}}x\] is

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