JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Analyzing +4 | -1

The derivative of

{\tan ^{ - 1}}\left( {\frac{{\sqrt {1 + {x^2}} - 1}}{x}} \right)

with respect to

{\tan ^{ - 1}}\left( {\frac{{2x\sqrt {1 - {x^2}} }}{{1 - 2{x^2}}}} \right)

x = \frac{1}{2}

View answer and explanation

Correct option: D

\frac{{\sqrt 3 }}{{10}}\,

Option D is correct because after simplification using trigonometric substitutions and differentiation, the derivative evaluates to

\frac{{\sqrt 3 }}{{{{10}}}}

x = \frac{1}{2}

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