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Differentiate each of the following func...

Differentiate each of the following functions with respect to `x :` (i) `sin^(-1)(2xsqrt(1-x^2)),-1/(sqrt(2))ltxlt1)`

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`sin^(-1)(2xsqrt(1-x^2)),-1/(sqrt(2))ltxlt1/(sqrt(2))`
`x=costheta`
`sin^(−1)(2sinθcosθ)=sin^(−1)sin2θ=2θ=2cos^(−1)x`
=`−π/2 ​≤ sin^(−1)(2xsqrt(1−x^2) ​) ≤ π/2`
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