check my work on derivatives
posted by Sarah on .
Can someone check my work?
So, I took the derivative of
(1x^2)/((1+x^2)^2)
I used the quotient rule
((2x((1+x^2)^2)2((1+x^2)^2)(2x)(1x^2))) / ((1+x^2)^4)
Then I simplified it
(2x+2x^2  4x((1+x^2)^2)(1x^2)) /((1+x^2)^4)
Then I simplified by factoring out some numbers
2x(x^2+1)[x^22(1x^2)]/((1+x^2)^4)
Then I cancelled out some values
2x[x^2+12(1x^2)]/((1+x^2)^3)
Then simplified some more
2x[x^2+12+2x^2)]/((1+x^2)^3)
2x[x^2+12+2x^2)]/((1+x^2)^3)
My answer was
2x(3x^21)/((1+x^2)^3)
But my answer is supposed to be
2x(x^23)/((1+x^2)^3)
Where did I go wrong

Well, the first line is wrong. Should be
((2x((1+x^2)^2)2(1+x^2)(2x)(1x^2))) / ((1+x^2)^4)
Maybe that's all the fix you need. If not, visit wolframalpha.com and enter
derivative (1x^2)/(1+x^2)^2
and it will show the correct answer which you show above. Then hit the stepbystep solution button to see all the intermediate work.