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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

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    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

    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
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