1. Not finding help here? Sign up for a free 30min 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!

Differential help

  1. Dec 26, 2012 #1
    The problem I am struggling with is differentiating f(r)=r/sqrt(r^2 + 1)

    I rewrote it as: r(r^2 +1)^(-1/2)
    Split this up to get:
    g(r)=r
    h(r)=(r^2 + 1)^(-1/2)

    By product rule, f'(r)=gh'+hg'

    Obviously
    g' = 1

    Now by chain rule, I find h'= -r(r^2 + 1)^-(3/2)

    Finally, I get f'= [(r^2 + 1)^(-1/2)] - [(r^2)((r^2 + 1)^(-3/2))]

    However, Several sources say this is not correct. I followed what I believe to be the right procedures, so any feedback on where I went wrong would be great. I'm doing this from mobile, so I can't show quite as much of my work as I want. Thanks in advance.
     
    Last edited: Dec 26, 2012
  2. jcsd
  3. Dec 26, 2012 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    This isn't true.

    This is true.

    This isn't true (likely because you have the incorrect form of g.
     
  4. Dec 26, 2012 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Also, did you mean to write [itex]f(r)=...[/itex] or [itex]f(x)=...[/itex].
    If you write

    [tex]f(x)=\frac{r}{\sqrt{r^2+1}}[/tex]

    then r is a constant, so f'(x)=0.
     
  5. Dec 26, 2012 #4
    I meant g' = 1, about to edit it. Everything else was in fact calculated assuming g'=1, it was simply a typing error
     
  6. Dec 26, 2012 #5
    fixed this too. it's f(r)
     
  7. Dec 26, 2012 #6

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    OK. But please don't edit your posts have there have been replies. It makes the thread difficult to read for future readers. Just make a new post with the corrections.

    Anyway:

    OK. Looking back at this, I think that it was correct after all. What sources say that it is incorrect??
     
  8. Dec 26, 2012 #7
    Solutions in the back of the book, wolframalpha. Apparently the answer is (r^2 +1)^(-3/2)
     
  9. Dec 26, 2012 #8

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Your answer is the same as that answer. Try to add up the fractions in

    [tex]\frac{1}{\sqrt{r^2 + 1}} - \frac{r^2}{\sqrt{(r^2+1)^3}}[/tex]
     
  10. Dec 26, 2012 #9
    Thanks! I didn't think to do that, thank you so much!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differential help
  1. Differentiation Help (Replies: 2)

  2. Differentiability help (Replies: 3)

  3. Differentiation help (Replies: 5)

Loading...