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Question
If `y=cos^-1(2xsqrt(1-x^2))`, find dy/dx
Solution
`y=cos^-1(2xsqrt(1-x^2))`
put `x=sintheta`
`theta =sin^-1x`
`=cos^-1(2sinthetasqrt(1-sin^2theta))`
`=cos^-1(sin2theta)`
`=cos^-1(cos(pi/2-2theta))`
`y=pi/2-2theta=pi/2-2sin^-1x`
Differentiating with respect to 'x', we get
`dy/dx=0 -2/sqrt(1-x^2) = (-2)/sqrt(1-x^2)`
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