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Chain rule and tangent vector

  1. Dec 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that:

    [tex] \frac{dx^\nu}{d \lambda} \partial_\nu \frac{dx^\mu}{d \lambda} = \frac{d^2 x^\mu}{d \lambda^2} [/tex]



    3. The attempt at a solution

    Well, I could simply cancel the dx^nu and get the desired result; that I do understand.
    But what about actually looking at this term alone:

    [tex]\partial_\nu \frac{dx^\mu}{d \lambda}, [/tex]

    calculating it and multiplying with dx^nu/dλ, can I get the same result? I get confused by the question: what if the partial derivative acts on the tangent vector; what happens then?


    Thanks for your help!!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 21, 2012 #2
    The problem is that [itex] \frac{d}{d\lambda} [/itex]and [itex] \partial_\mu [/itex] do not commute... So I'm not sure how you could calculate it without knowing what [itex] \frac{d}{d\lambda} [/itex] is.
     
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