Differentiate `sin^(-1)(3x-4x^3)` with respect to `x` , if `1/2ltxlt1`

Explanation

Given that,
`y=sin^(-1)(3x-4x^3)`
`x=sin theta`
`=>y=sin^-1 (3sintheta-4 sin^3 theta )`
`=>y=sin^-1[sin 3theta]`
`1/2lt sin theta lt1`
or`pi/6 lt theta lt pi/2`
or`pi/2 lt 3theta lt (3pi)/2`
or`-pi/2 lt pi-3theta lt pi/2`
so,`y=sin^-1[sin 3theta]`
`=sin^-1 [sin(pi-3theta)]`
`=>y=pi-3theta`
`=>y=pi-3 sin^-1 x`
`(dy)/(dx)= -3/sqrt(1-x^2)`