Hi, I got the right answer when I used the Quotient Rule but not when I used the Product Rule... I think it might be an algebra mistake... Product Rule Method: f'(x) = (3 - x^2)*(4 + x^2)^-1 = (3 - x^2)[(-1(4 + x^2)^-2)*2x] + [(4 + x^2)^-1](-2x) = [(3 - x^2)(-2x)]/[(4 + x^2)^2] + [(-2x)/(4 + x^2)] To get the same denominator here, I thought I might square the factor on the right. = (-6x + 2x^3 + 4x^2)/[(4 + x^2)^2] <----- This is not right. THE RIGHT ANSWER IS: -14x/[(4 + x^2)^2] I found that by using the Quotient Rule. ...But where am I going wrong with the Product Rule...? P.S. Oh, and a side note: If I wrote out the Product Rule answer like this: (-6x + 2x^3 + 4x^2)/(x^4 + 8x^2 + 16) Would the 4x^2 and the 8x^2 be able to cancel somewhat? Sometimes I get confused about what can cancel. Could it turn into: (-6x + 2x^3)/(x^4 + 2 + 16) = (-6x + 2x^3)/(x^4 + 18)? I know that's not the right answer, but is this how it would cancel? Thank you very much!