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Differentiation of dot product using cartesian components

  1. Nov 12, 2008 #1
    1. The problem statement, all variables and given/known data

    Show using cartesian components that

    d/dt(a.b)=(da/dt).b+a.(da/dt)



    3. The attempt at a solution

    a= axi+ayj+azk
    b=bxi+byj+bzk

    a.b=axbx+ayby+azbz

    d/dt(a.b)= d/dt(axbx+ayby+azbz)
     
  2. jcsd
  3. Nov 12, 2008 #2

    HallsofIvy

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    Okay, so go ahead and do that! Use the sum rule and product rule.
     
  4. Nov 12, 2008 #3
    Heya, thanks for the reply.

    So ive done that nd nw iv got

    (da/dt)b+(db/dt)a

    do i just put this as the dot product or have i missed out something in my equation?
     
  5. Nov 12, 2008 #4
    Since you're talking about putting this as a dot product I assume by writing (da/dt)b you meant some different "product" of the two vectors da/dt and b. May I inquire what exactly you were thinking of and how it is related to the dot product (which is where you started from.)
     
  6. Nov 12, 2008 #5
    oh, i see now, i wasn't thinking of them as two vectors but as mulitplying two scalars.

    i just forgot what it was i was working with, sorry.

    Thanks alot for your help though, really appreciate it.
     
  7. Nov 12, 2008 #6
    It sometimes happens to be useful to pay attention to exactly this particular issue:smile:
     
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