#### Question

If `y=cos^-1(2xsqrt(1-x^2))`, find dy/dx

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#### Solution

`y=cos^-1(2xsqrt(1-x^2))`

put `x=sintheta`

`theta =sin^-1x`

`y=cos^-1(2xsqrt(1-x^2))`

`=cos^-1(2sinthetasqrt(1-sin^2theta))`

`=cos^-1(2sintheta costheta)`

`=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=-2/sqrt(1-x^2)`

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Solution for question: If y=cos^-1(2xsqrt(1-x^2)), find dy/dx concept: null - Derivative of Inverse Function. For the courses HSC Science (General) , HSC Science (Computer Science), HSC Science (Electronics), HSC Arts