No, that is not correct. Assuming you mean ((x+1)^2- 2x^2(x+1))/(x+1)^4, you should not have that "^2" in "-2x^2(x+1)". The derivative of (x+1)^2 is 2(x+1) and, using the quotient rule, you just multiply that derivative by the numerator, x.

Well,What are the intervals?

Thanks!whydid you differentiate? What is true about the derivative of a function where the function is increasing? What if the function is decreasing?