I know this is a very basic question but I need some help.
I have to find the second derivative of:
$$\frac{1}{3x^2 + 4}$$
I start by using the Quotient Rule and get the first derivative to be:
$$\frac{-6x}{(3x^2 + 4)^2}$$
This I believe to be correct. Following that I proceed to find the second derivative in the same manner but I get this as my answer: $$\frac{(54x^4 + 144x^2 +96) - (-36x^3 + 48x)}{(9x^4 +24x^2 +16)^2}$$
This I believe to be correct just not simplified. However the answer I need to get is: $$- \frac{6(4 - 9x^2)}{(3x^2 + 4)^3}$$ I do not know what the best way to approach this would be, should I multiply out the denominator and try to cancel? Could someone point me in the right direction, I want to solve it myself but I need some guidance.
Thanks