Find the derivative of (4x^3-3x^2+x+1)^1/2 /(x+1)^2 pls i need detailed explanation

Answer 1

first line derivative using the quotient rule ....

((x+1)^2 (1/2)(4x^3-3x^2+x+1)^(-1/2) (12x^2-6x+1) - ((4x^3-3x^2+x+1))^(1/2) (2)(x+1))/(x+1)^4

= (1/2)(x+1)(4x^3-3x^2+x+1)^(-1/2) [(x+1)(12x^2 - 6x + 1) - 4(4x^3-3x^2+x+1) ] / (x+1)^4

= (1/2)(4x^3-3x^2+x+1)^(-1/2) (-4x^3 + 18x^2 - 9x - 3) / (x+1)^3

I think you better check my algebra, very easy to make a typo in this mess.