Question

$y = { \sec}^{ - 1} ( \frac{1}{1 - 2 {x}^{2} } ) \: \: find \: \: \frac{dy}{dx}$
How to solve this one ?​

Answer 1

Step-by-step explanation:

We have,

$y = \sec^{ - 1} ( \frac{1}{1 - 2 {x}^{2} } )$

Let x= sin(θ)

$\implies y = \sec^{ - 1} ( \frac{1}{1 - 2 \sin^{2} ( \theta) } )$

$\implies y = \sec^{ - 1} ( \frac{1}{\cos( 2\theta) } )$

$\implies y = \sec^{ - 1} ( \sec ( 2\theta) )$

$\implies y = 2 \sin ^{ - 1} (x)$

$\implies \frac{dy}{dx} = \frac{ 2}{ \sqrt{1 - {x}^{2} } }$