Question

How do you find the derivative of

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

?

I have the answer which is:
(4x(3+x^2))/(x^2-1)^3)

I can't figure out my mistake when I'm doing it though. Could you solve it step by step?

Answer 1

You don't show your intermediate steps, but you have to use the quotient rule to get
dy/dx = [ -4x(x^2-1)^2 + 2(x^2+1)^2 (2)(x^2-1)(2x)]/(x^2-1)^4
= -4x(x^1 - 1) [(x^2 - 1) - 2(x^2+1)]/(x^2-1)^4
= -4x[-x^2 - 3)/(x^2-1)^3
or 4x(x^2 + 3)/(x^2 - 1)^3 which is your answer !
or
= (4x^3 + 12x)/(x^2 - 1)^3

I don't know what answer was expected.