. y = - 1 ( 2 x 2 - 1 ),0 < x < 2 .

Putting x = , we get y = - 1 ( 2 2 - 1 ) y = - 1 (2 2 - 1) y = - 1 ( 2 ) y = 2 y = 2 - 1 x dx = - [couleur = blue!30, arrondi = 0.1 ] NCERT - Exercise 5.4 Differentiate the following w.r.t. x ;

Continuity and Differentiability — Class 12 Maths Solution

ncert exercise SA NCERT Ex.5.3 ,Q.15,Page 169

Question

. $y = {\sec ^{ - 1}}\left( {\cfrac{1}{{2{x^2} - 1}}} \right),0 < x < \cfrac{1}{{\sqrt 2 .}}$

Step-by-step Solution

Putting $x = \cos \theta ,$ we get

$y = {\sec ^{ - 1}}\left( {\cfrac{1}{{2{{\cos }^2}\theta - 1}}} \right)$

$\Rightarrow$ $y = {\cos ^{ - 1}}(2{\cos ^2}\theta - 1)$
$\Rightarrow$ $y = {\cos ^{ - 1}}(\cos 2\theta )$

$\Rightarrow$ $y = 2\theta \Rightarrow y = 2{\cos ^{ - 1}}x$
$\Rightarrow$ $\cfrac{{dy}}{{dx}} = - \cfrac{2}{{\sqrt {1 - {x^2}} }}$

$figure$

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