Can someone check my work?

Question

So, I took the derivative of
(1-x^2)/((1+x^2)^2)

I used the quotient rule

((2x((1+x^2)^2)-2((1+x^2)^2)(2x)(1-x^2))) / ((1+x^2)^4)

Then I simplified it

(2x+2x^2 - 4x((1+x^2)^2)(1-x^2)) /((1+x^2)^4)

Then I simplified by factoring out some numbers

2x(x^2+1)[x^2-2(1-x^2)]/((1+x^2)^4)

Then I cancelled out some values

2x[x^2+1-2(1-x^2)]/((1+x^2)^3)

Then simplified some more

2x[x^2+1-2+2x^2)]/((1+x^2)^3)

2x[x^2+1-2+2x^2)]/((1+x^2)^3)

My answer was

2x(3x^2-1)/((1+x^2)^3)

But my answer is supposed to be

2x(x^2-3)/((1+x^2)^3)

Where did I go wrong

Answer 1

Well, the first line is wrong. Should be

((-2x((1+x^2)^2)-2(1+x^2)(2x)(1-x^2))) / ((1+x^2)^4)

Maybe that's all the fix you need. If not, visit wolframalpha.com and enter

derivative (1-x^2)/(1+x^2)^2

and it will show the correct answer which you show above. Then hit the step-by-step solution button to see all the intermediate work.