Find the intervals on which y=1/(x^2+1)^2 is increasing and decreasing.

Question

find the first derivative which is
-4x/(x^2+1)^3

you should know that if the first derivative is positive, then the function is increasing and if it is negative, the function is decreasing.

Now by inspection look at this derivative.
The denominator is always positive.

If x is positive, the numerator is negative, so the function decreases for positive x's
and conversely the function increases for positive values of x

I see what I did wrong now, thank you for your help.