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Differentiate cos^(-1)(2x^2-1) with res...

Differentiate `cos^(-1)(2x^2-1)` with respect to `x` , if `0ltxlt1`

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Verified by Experts

given that,
`cos^(-1)(2x^2-1)`,`0ltxlt1`
let`x=cos theta`
`y=cos^-1 (2cos ^2 theta -1)`
`=>y=cos^-1 (cos 2 theta)`
`0 lt cos theta lt 1`
or`0 lt theta lt pi/2`
or `0 lt 2theta lt pi`
so,`y=2theta`
`=>y=2 cos ^-1 x`
`(dy)/(dx)=-2/sqrt(1-x^2)`
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