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!

Simple differential questions

  1. Feb 29, 2008 #1
    A little thing that may be stupid but I am confused about it. Say we take any equation like f=ma
    If we take the derivative of both sides then we could either have

    df=m da
    or
    df =a dm

    Are both of these valid computations. If I am looking to change the integrating variable can I use this any way I want? And would this work with any equation relating 3 or more variables?

    thanks in advanced
     
  2. jcsd
  3. Feb 29, 2008 #2

    Andy Resnick

    User Avatar
    Science Advisor
    Education Advisor
    2016 Award

    You are basically correct: the "rocket equation" comes from F = dp/dt = d(mv)dt = m dv/dt + v dm/dt.

    For what you wrote, f = ma, df = m da/dt + a dm/dt.
     
  4. Feb 29, 2008 #3

    pam

    User Avatar

    If f=abc, df=ab dc+ ac db + bc da, and so on for an number of variables.
    You just differentiate one at a time.
    Of course if any factor is a constant, then its differential is zero.
     
  5. Feb 29, 2008 #4

    pam

    User Avatar

    The "rocket equation" is a bit different, because the exit velocity of the gas enters instead of just v in the dm/dt term.
     
  6. Feb 29, 2008 #5
    thanks this clears some up. But as I said before could I take df=mda to subsitute df with da to integrate with respect to a, and in the same problem could I take df=adm to integrate with respect to m.

    so you could take s=rTheta and make it ds=rdtheta?

    I'm just seeing how flexible I can be when substituting vaiables to integrate or differentiate with.

    Edit, I just realized that what you did there was the product rule which makes sense. Is what I just said above wrong then?>
     
    Last edited: Feb 29, 2008
  7. Feb 29, 2008 #6

    pam

    User Avatar

    A derivative of all product of N variables will have N terms, each term being differentilated once. So d(r theta)=r dtheta+theta dr.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simple differential questions
  1. Simple Question? (Replies: 5)

  2. Simple question (Replies: 3)

Loading...