Question

use the quotient rule to find derivative.

y= 3x^2+8 / x^2+3

(x^2+3)(6x) - (3x^2+8)(2x) all over (x^2+3)^2

The answer is 2x/(x^2+3)^2

The only problem is I am not sure how they simplified this to get the answer.

Answer 1

Just expand and simplify your numerator.

[(x^2+3)(6x) - (3x^2+8)(2x)] / (x^2+3)^2
= (6x^3 + 18x - 6x^3 - 16x)/(x^2+3)^2
= 2x/(x^2+3)^2