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!

Working out the first and second derivative

  1. Apr 27, 2009 #1
    Let f(x)=x^2/(1-x^2 )
    a) Find f'(x)
    b) Find f"(x)

    For the answer to a) they give f'(x)=2x/〖(1-x^2)〗^2
    and for b) f"(x)=2 (1+〖3x〗^2)/〖(1-x^2)〗^3

    Now after many rounds of trying i have not been able to get an answer remotely close to what they have given. i don;t know if it is due to me over working a simple problem or what. the same applies to b), taking the second derivative.

    For a) i applied the quotient rule:

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

    then it stops there as i don't know where to proceed, i am not entirely sure if what i have done is correct but other methods result in something similar.

    Then for b)

    f'(x)=2x/〖(1-x^2)〗^2

    Using their answer and trying to work with it to see if i fared any better for the 2nd derivative proved that i was lost. any help with a) would be appreciated as it means i could work out b) and any similar problems in the future.
     
  2. jcsd
  3. Apr 27, 2009 #2
    You seem to have made an error in applying the quotient rule. You should have
    f'(x)=[g'(x)h(x)-h'(x)g(x)]/[h(x)]^2 where g(x)=x^2 and h(x)=1-x^2. After you differentiate h(x) where I suggested, multiply the resulting numerator all out and combine like terms.

    I confirmed the answer to a) but I think the answer for b) should be
    f"(x)=2 (1+3〖x〗^2)/〖(1-x^2)〗^3

    Personally, I never use the quotient rule. Note that you can write any function that readily permits the quotient rule (i.e. f(x)=g(x)/h(x)) as f(x)=g(x)[h(x)]^(-1) and then apply the product rule. However, it is important to realize the inner workings of the quotient rule for problems that specifically call for its use (tends to happen a lot on calculus midterms//finals//what have you).
     
  4. Apr 28, 2009 #3
    Thank you, for some reason something wasn't clicking.
    Found using the product rule with these problems really simplifies them so, thanks again.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Working out the first and second derivative
Loading...