Find dy/dx for y = (4x^2 - 2) / (x^3 - 1)

We have to find the derivative of y = (4x^2 - 2) / (x^3 -
1)

y = (4x^2 - 2) / (x^3 -
1)

=> (4x^2 - 2)*(x^3 -
1)^-1

Use the product rule for
differentiation

y' = [(4x^2 - 2)]'*(x^3 - 1)^-1 + (4x^2 -
2)*[(x^3 - 1)^-1]'

=> (8x)*(x^3 - 1)^-1 + (4x^2 -
2)*-1*[(x^3 - 1)^-2]*3x^2

=> [(8x)*(x^3 - 1) + (4x^2
- 2)*-1*3x^2]/[(x^3 - 1)^2]

=> [(8x^4 - 8x - 12x^4 +
6x^2]/[(x^3 - 1)^2]

=> [(-4x^4 + 6x^2 - 8x]/[(x^3 -
1)^2]

The value of dy/dx = [(-4x^4 + 6x^2 -
8x]/[(x^3 - 1)^2]