The question asks to find increasing/decreasing/concave up/concave down for:

(5x)/(x^2+1)

So I found the first derivative using the quotient rule:

[5(x^2+1)-5x(2x)]/[(x^2+1)^2]

Simplified, I got it down to

[-5x^2+5]\[(x^2+1)^2]

Got a critical point at x=1, and did a first derivate sign test to find increasing/decreasing. Came out to increasing: (-i, 1] and decreasing: [1, i)

On to concavity, which is found through the second derivative. This is where I am stumped. The algebra is killing me, or I could've messed up on the first derivate. Anyway, without simplification I got:

[-10x(x^2+1)^2]-[(-5x^2+5)(2(x^2+1)(2x))]

Could someone help me simplify that, it's killing me :mad:

Thanks in advance!