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The derivation of \(\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)\) with respect to \(\tan ^{-1}\left(\frac{2 x \sqrt{…

Q1
PYQ

The derivation of \(\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)\) with respect to \(\tan ^{-1}\left(\frac{2 x \sqrt{1-x^2}}{1-2 x^2}\right)\) at \(x=\frac{1}{2}\) is:

[JEE Main 2020, 5 Sep (Shift 2)]

a

\(\frac{2 \sqrt{3}}{3}\)

b

\(\frac{\sqrt{3}}{10}\)

c

\(\frac{\sqrt{3}}{12}\)

d

\(\frac{2 \sqrt{3}}{5}\)

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