Question

How do you derive `y = (4x^4 − 2) / (-x^2 + 1)` using the quotient rule?

Answer 1

`(dy)/(dx)=(16x^3-8x^5-4x)/(-x^2+1)^2`

Explanation:

`y=(4x^4-2)/(-x^2+1)`

`(dy)/(dx)=((-x^2+1)(16x^3)-(4x^4-2)(-2x))/(-x^2+1)^2`

`(dy)/(dx)=(-16x^5+16x^3+8x^5-4x)/(-x^2+1)^2`

`(dy)/(dx)=(16x^3-8x^5-4x)/(-x^2+1)^2`