The derivative of `cos^(-1)(2x^2-1)` with respect to `cos^(-1)x` is (a) 2 (b) `1/(2sqrt(1-x^2))` (c) `2//x` (d) `1-x^2`

Explanation

Considering `u = cos^(–1) (2x^2 – 1)`

Put `x = cos theta ⇒ theta = cos^(-1)x ---(1)`

` u = cos^(–1) (2cos^2theta– 1)`

` u = cos^(–1) (cos2theta)`

`∵ 2cos^2theta – 1 = cos^2theta`
`u = 2theta`

`u = 2 cos^(-1)x -- From(1)`

Differentiating w.r.t x we get,

`frac{dv}{dx}=-frac{1}{sqrt(1-x^2)}`
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