Given the function, y =t/(t^2+1), find d^2 y/dt^2?

dy/dt is given by :-

(t² + 1) - 2t²
----------------
[ t² + 1 ]²

1 - t²
------------
[ t² + 1 ]²

d[²y/dt² is then given by :-

[ t² + 1 ]² [ - 2t ] - [ 1 - t² ] 2 [ t² + 1 ][ 2t ]
---------------------------------------------------
[ t² + 1 ]^4

[-2t] [ t² + 1 ]² - [ 4t ] [ 1 - t² ] [ t² + 1 ]
----------------------------------------------------
[ t² + 1 ]^4

[ -2t ] [ t² + 1 ] [ 3 - t² ]
------------------------------
[ t² + 1 ]^4

[ - 2t ] [ 3 - t² ]
---------------------
[ t² + 1 ]^3

[ 2t ] [ t² - 3 ]
------------------
[ t² + 1 ]^3