Problem on finding second derivative.

[jzq]

I have a problem on finding the second derivative for this function:

$$\frac {x}{x^2-4}$$

For the first derivative, I got:

$$\frac {-x^2-4}{(x^2-4)^2}$$

Now here is where I am stuck! So far for the second derivative, I got this (Please check!):

$$\frac {-2x(x^2-4)^2-4x(-x^2-4)(x^2-4)}{(x^2-4)^4}$$

I need the second derivative simplified! I know, it's an easy question. I may have lost my mind!
Also please explain. Thanks!

BTW. I am new to this forum and just learned the latex system. It is very complicated. Took me a while just to write out the problems above. I guess I got to get used to it.

 

[Davorak]

Those look good to me. Now all you need to do is simplify. That should be the easy step. You have a factor of $(x^2-4)$ that will divide out. You should be able to get it down to one term.

 

[jzq]

Those look good to me. Now all you need to do is simplify. That should be the easy step. You have a factor of $(x^2-4)$ that will divide out. You should be able to get it down to one term.

Is this what you got?:

$$\frac {2x^3+24x}{(x^2-4)^3}$$ or $$\frac {2x(x^2+12)}{(x^2-4)^3}$$

 

[Davorak]

Looks good