1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

2nd derivative trouble

  1. Aug 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Find horiz. asymptotes and use them w/ concavity and intervals to sketch the curve

    2. Relevant equations

    3. The attempt at a solutionf'(x)= 1-x^2/(x^2+1)^2
    But then I can't seem to work through taking the 2nd derivative, perhaps I am not using the chain rule right.
    I get -4x^5-2x^3-2x/(x^2+1)^4
    But thats not right... please help!
  2. jcsd
  3. Aug 25, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Assuming you meant f(x)=x/(x^2+1) and not f(x)=(x/x^2)+1, the first derivative is correct. So again using the quotient rule, the second derivative will be
    [tex]\frac{ (1 - x^2)' (x^2 + 1)^2 - (1 - x^2) ((x^2 + 1)^2 )' }{(x^2+1)^4}[/tex]
    Can you work out the two derivatives that are there separately?
  4. Aug 25, 2008 #3
    So I get that f''(x)= ((-2x)((x^2+1)^2)-1-x^2)((2)(x^2+1))(2x))/(x^2+1)^4
    I think thats right but not sure about distributing through.

    I get (2x^5-2x^3-4x)/(x^2+1)^4

    But the posted answer is (2x^5-4x^3-6x)/(x^2+1)^4
  5. Aug 25, 2008 #4


    User Avatar
    Science Advisor
    Homework Helper

    The first line is correct, so you probably did something wrong in the expansion.
    Try working out
    separately, and only then adding them.
    Forgetting about the denominator (x^2 + 1)^4 for a while, you should get 2 x^5 - 4x^3 - 6x.

    And look at the bright side: probably it's some stupid writing error, at least you know you can differentiate :smile:
  6. Aug 25, 2008 #5
    Thanks for all the help, most of my errors are in the algebra...
    on the left side I get (-2x^5-2x) and the right -((1-x^2)(4x^3+4x)) which goes to -(4x^3+4x-4x^5-4x^3).... Left - Right I get 2x^5-6x!! still missing the -4x^3 I don't know where i am going wrong.
  7. Aug 26, 2008 #6


    User Avatar
    Science Advisor
    Homework Helper

    You do? I don't.
    What does (x^2 + 1)^2 expand to? It's not x^4 + 1!
    If you want, write it out: (a + b)^2 = (a + b)(a + b) = ....
    Then remember that formula (or at least, remember to remember that something is going on whenever you see it) forever :smile:
  8. Aug 26, 2008 #7
    now I understand....I was convinced my mistake was on the right not the left. Thanks a ton.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: 2nd derivative trouble
  1. 2nd Derivative (Replies: 12)

  2. 2nd derivative (Replies: 1)

  3. 2nd derivatives (Replies: 4)