If f(x) = sin (cos ⁻¹((1 - 2²ˣ)/(1 + 2²ˣ))) and its first derivative with respect to x is - b/a log e 2 when x = 1, where a and b are integers, then the minimum value of | a² - b² | is _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 17 Mar, Morning shift · Q32

JEE Main 202117 Mar, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

f(x) = \sin \left( {{{\cos }^{ - 1}}\left( {{{1 - {2^{2x}}} \over {1 + {2^{2x}}}}} \right)} \right)

and its first derivative with respect to x is

- {b \over a}{\log _e}2

when x = 1, where a and b are integers, then the minimum value of | a²

-

b² | is ____________ .

Your answerType your answer. Integers and decimals are accepted.