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If y=sec^(-1)(1/(2x^2-1));0<x<1/(sqrt(2)...

If `y=sec^(-1)(1/(2x^2-1));0

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The correct Answer is:
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Let ` y =sec^(-1)((1)/(4x^(3)-3x))"....."(i)`
On putting `x = costheta` in Eq. ( i), we get
`y = sec^(-1)(1)/(4cos^(3)theta-3costheta)`
`= sec^(-1)'(1)/(cos3theta)`
`= sec^(-1)(se3 theta)= 3 theta`
`= 3 cos^(-1)x [:' theta = cos^(-1)x]`
`:. (dy)/(dx) = (d)/(dx) (3cos^(-1)x)`
` = 3.(-1)/(sqrt(1-x^(2)))`
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