given the curve y=2x/(1+x^2)^2
(a) prove that dy/dx =2(1-x^2)/(1+x^2)^2
(b) find the coordinates of the stationary points and state the nature of the stationary points.
I will write it as y = 2x(1+x^2)^-2 and use the product rule
a)
dy/dx = 2x(-2)(1+x^2)^-3 (2x) + 2(1+x^2)^-2
= 2(1+x^2)^-3 [ -4x^2 + 1+x^2]
= 2(1 - 3x^2)/(1+x^2)^3
confirmed by Wolfram
http://www.wolframalpha.com/input/?i=derivative+of+y+%3D+2x%2F%281%2Bx%5E2%29%5E2
check your typing, I suspect a typo in either the original equation or in your dy/dx