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

Answer

N/a

Explanation

Let ` 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)(se3 theta)= 3 theta`
`= 3 cos^(-1)x [:' theta = cos^(-1)x]`
`:. (dy)/(dx) = (d)/(dx) (3cos^(-1)x)`
` = 3.(-1)/(sqrt(1-x^(2)))`