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!

Gradient vector problem

  1. Sep 5, 2011 #1
    1. The problem statement, all variables and given/known data

    If [itex]z = f(x,y)[/itex] such that [itex]x = r + t[/itex] and [itex]y = e^{rt}[/itex], then determine [itex]\nabla f(r,t)[/itex]

    2. Relevant equations

    [itex]\nabla f(x,y) = <f_x,f_y>[/itex]

    3. The attempt at a solution

    Now if i follow this the way i think it should be done then i find the partials of f wrt x and y and then simply sub in r and t in the place of x and y respectively...

    But if i get del f the normal way i get:

    [itex]\nabla f = <f_x+f_y t e^{rt},f_x+f_y r e^{rt}>[/itex]

    is this the final/correct answer or am i missing a trick question where i was asked to find del f(r,t) and not del f(x,y)
     
  2. jcsd
  3. Sep 5, 2011 #2

    I like Serena

    User Avatar
    Homework Helper

    Welcome to FP, evo_vil! :smile:

    Your problem is ambiguous.
    If I take it very literal, the answer would be:
    [tex]\nabla f(r,t)=<f_x(r,t), f_y(r,t)>[/tex]

    However, I can't imagine that this was intended.

    I expect that you're supposed to take the gradient from a function f* defined by:
    f*(r,t) = f(x(r,t), y(r,t)).
    It is not unusual that this function f* is simply called f, although that is ambiguous.

    This is what you calculated, and no doubt correct.
     
  4. Sep 5, 2011 #3
    Thanks!

    Ive browsed PF for quite a few years, but never participated, so thanks for the welcome...

    I think im just going to go with what ive calculated and see how it goes...
    Maybe see if other people get the same thing.

    Thanks for your help
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Gradient vector problem
  1. Gradient vector (Replies: 2)

  2. Gradient vectors (Replies: 2)

  3. Gradient Vectors (Replies: 21)

Loading...