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

Explanation

given that
`y=cos^(-1)(4x^3-3x)`
` y =sec^(-1)((1)/(4x^(3)-3x))"....."(i)`
On putting `x = costheta` in Eq. ( i), we get
`y = sec^(-1)(1)/(4cos^(3)theta-3costheta)`
`= sec^(-1)(1)/(cos3theta)`
`= sec^(-1)(sec theta)= 2pi-3 theta`
`= 2pi-3 cos^(-1)x `
`:. (dy)/(dx) = (d)/(dx) (2pi-3cos^(-1)x)`
` = 3.(1)/(sqrt(1-x^(2)))`