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Thread: Concepts of relationships of fcns & their deriv's: w = f(x,y,z)= f(r(t)) = g(t)

  1. #1
    Junior Member
    Join Date
    Mar 2010
    Posts
    79

    Concepts of relationships of fcns & their deriv's: w = f(x,y,z)= f(r(t)) = g(t)

    Hello All,

    Given:
    f : R3→R

    r : R→ R3represents position of moving object as a function of time

    g(t) is valueof f at the objectís position at time t



    Firstquestion:
    Is all thiscorrect for me to say:
    w = f(x,y,z)= f(r(t)) = g(t)


    Secondquestion:
    Are partialderivatives of w and of f the same, in other words, do:
    ∂w/∂x = ∂f/∂xand ∂w/∂y = ∂f/∂y and ∂w/∂z = ∂f/∂z

    Thirdquestion:

    Arederivatives with respect to t all equal, in other words, do:
    df/dt = dg/dt= dw/dt

    Trying tounderstand correct concepts and relationships between all the elements of thisexercise, so I hope my questions make sense.

    Thank you


  2. #2
    Junior Member
    Join Date
    Mar 2010
    Posts
    79
    Hello All,
    Can ignore this.
    I was able to confirm answers to all 3 questions are all "yes".
    Thank you

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