if y = (3x^3 -12x^2 + 2x -8)/(x-4)
find the derivative y'
When given a problem like this, it is probably easier to divide first rather than use the Quotient Rule.
If you factor the numerator, you find that it equals
(3x^2(x-4) + 2(x-4))
=(3x^2 + 2)(x-4)
Dividing by (x-4), the polynomial becomes (3x^2 + 2)
y = 3x^2 + 2
y' = 6x (power rule)