Find the derivative of y = x/(1+x^2),,,,(check my work)?

Question

[(1+x^2)x' - x(1+x^2)'] / [(1+x^2)^2]
[x(1) - x(0 + x)] / [(1+x^2)^2]
(-x^2 + x)/ [(1+x^2)^2]

Could someone help me understand what I am doing wrong?

Answer 1

derive x, multiply by the bottom and subtract the derivative of the bottom multiplied by x:

y'=(1+x^2)-(2x)x / (1+x^2)^2

you got the denominator right...
The derivative of 1+x^2 is not x, it is 2x.

and its simple math from there.

Answer 2

y = x/(1+x^2)
y' = [(1+x^2)(1) -x(2x)]/(1+x^2)^2
= (x^2-2x+1)/(1+x^2)^2
=(x-1)^2/(1+x^2)^2