Differentiate `(x^(2)-x+1)/(x^(2)+x+1)` with respect to 'x'.

Explanation

Let `y=(x^(2)-x+1)/(x^(2)+x+1)`
`rArr(dy)/(dx)=(d)/(dx)((x^(2)-x+1)/(x^(2)+x+1))`
`(X^(2)+x+1)(d)/(dx)(x^(2)-x+1)`
`=(-(x^(2)-x+1)(d)/(dx)(x^(2)+x+1))/((x^(2)+x+1)^(2))`
`=((x^(2)+x+1)(2x-1)-(x^(2)-x+1)(2x+1))/((x^(2)+x+1)^(2))`
`=((2x^(3)+x^(2)+x-1)-(x^(2)-x+1)(2x+1))/((x^(2)+x+1)^(2))`
`=((2x^(3)+x^(2)+x-1)-(2x^(3)-x^(2)+x+1))/((x^(2)+x+1)^(2))`
`=(2(x^(2)-1))/((x^(2)+x+1)^(2))`