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  4. Derivative of sec -1 (1/2 x2-1) w.r.t. √1-x2 at x =1 / 2 is

Q. Derivative of $\sec ^{-1}\left\{\frac{1}{2 x^{2}-1}\right\}$ w.r.t. $\sqrt{1-x^{2}}$ at $x =1 / 2$ is

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Solution:

$y^{1}=x^{2}-3 x+2=0$
$\Rightarrow(x-1)(x-2)=0 $
$\therefore x=1,2 ; $ at $x=1, y=-7 / 6$

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