Question

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

Answer 1

`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)`