I need help deriving this function:

g(t)=tan^-1 (t/ sqrt(2 - t^2))

Any help would be appreciated! Thanks

What I got when I tried deriving it:

1/(1+(t/sqrt(2-t^2))^2) x (sqrt(2-t^2)+(t^2/(sqrt(2-t^2)))/(sqrt(2-t^2))

and eventually ended up with:

2/((sqrt(2-t^2))^3 + t^3(sqrt(2-t^2)))