How do I differentiate y = x^2/1-x^2 correctly?

[Hollysmoke]

I just wanted to make sure I differentiated this correctly before I started graphing it:

y=x^2/1-x^2

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

y''=(2+6x^2)/(1-x^2)^3

 

[Hootenanny]

I just wanted to make sure I differentiated this correctly before I started graphing it:

y=x^2/1-x^2

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

y''=(2+6x^2)/(1-x^2)^3

I don't think that it is quite correct. I believe you are missing a term for your y' derivative (I haven't checked your y''). How did you differentiate? Using the quotient rule?

 

[Hollysmoke]

Yes, I used the quotient rule:

y'= (1-x^2)(2x)-(-2x)(x^2) / (1-x^2)
y'= 2x-2x^3+2x^3 / (1-x^2)

 

[arunbg]

Don't forget to square the denominator ;)