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!

Finding the second derivative of multvariable function

  1. Nov 1, 2007 #1
    Hello I am trying to figure out the second derivative of

    [tex] \frac{\partial^2 z}{\partial x^2}[/tex] and [tex] \frac{\partial^2 z}{\partial t^2}[/tex]

    z(u) and u=x-vt

    i found the first derivate of [tex] \frac{\partial z}{\partial x}[/tex] to be
    [tex] \frac{\partial z}{\partial x}[/tex]= [tex] \frac{\partial z}{\partial u}[/tex] * [tex] \frac{\partial u}{\partial x}[/tex] = [tex] \frac{\partial z}{\partial u}[/tex] *1

    and

    [tex] \frac{\partial z}{\partial t}[/tex] = [tex] \frac{\partial z}{\partial u}[/tex] * [tex] \frac{\partial u}{\partial t}[/tex]= [tex] \frac{\partial z}{\partial u}[/tex]*v

    after this i am clueless on how to compute
    ([tex] \frac{\partial }{\partial t}[/tex])[tex] \frac{\partial z}{\partial u}[/tex]*v
    and
    ([tex] \frac{\partial }{\partial x}[/tex])[tex] \frac{\partial z}{\partial u}[/tex]*1

    i am new here am hoping to receive some help i will greatly appreciate it!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 1, 2007 #2
    Are you trying to say that z(u)=x-vt?
     
  4. Nov 1, 2007 #3
    i guess the answer should be for [tex] \frac{\partial^2 z}{\partial t^2}[/tex] = v^2 * [tex] \frac{\partial^2t }{\partial u^2}[/tex]

    im not sure at all how to get this tho any help?
     
  5. Nov 1, 2007 #4
    i guess im trying to say that z is a function of u and u is a function of x and t
     
  6. Nov 2, 2007 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    No, since u= x- vt, [itex]\partial u/\partial t= -v[/itex], not v.

    The "v" and "1" are constants. So you are just differentiating a function of x and t again:
    [tex]\frac{\partial}{\partial x}\frac{\partial z}{\partial u}= \frac{\partial^2 z}{\partial u^2}\frac{\partial u}{\partial x}[/tex]
    and, of course, [itex]\partial u/\partial x[/itex] is 1.

    Likewise
    [tex]\frac{\partial}{\partial t}\frac{\partial z}{\partial u}= \frac{\partial^2 z}{\partial u^2}\frac{\partial u}{\partial t}[/tex]
    and [itex]\partial u/\partial t[/itex] is -v.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Finding the second derivative of multvariable function
Loading...