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A particle moves on a surface find ∂x/∂y at given point

  1. Nov 28, 2011 #1
    1. The problem statement, all variables and given/known data

    A particle moves on the surface (z^2)/2+yz-(x^2)/2=2. At point (-2, 1, 2) x is changing at the rate of 2/m sec and z is changing at the rate of -1/m sec. Determine in m/sec. the rate of change (with respect to time) of ∂x/∂z at (-2, 1, 2).

    2. Relevant equations



    3. The attempt at a solution
    Not really sure where to start and all my attempts get me nowhere. Does ∂x/∂t = 2 and ∂z/∂t = -1? I tried that and then differentiated with respect to t and got nowhere. If someone could help me in the right direction that would be great. Thanks for your time.
     
  2. jcsd
  3. Nov 28, 2011 #2

    HallsofIvy

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    Frankly, the phrase "the rate of change (with respect to time) of ∂x/∂z" doesn't make much sense to me. I guess it would mean
    [tex]\frac{d\frac{\left(\partial x\right)}{\partial z}}{dt}[/tex]
    but that looks very peculiar.

    An obvious problem would be to find the rate of change of y with respect to t.
     
  4. Nov 28, 2011 #3
    That's what confuses me a bit. How can you find ∂x/∂z though?
     
  5. Nov 28, 2011 #4
    Ok can someone correct me if this idea is completely wrong. Can ∂x/∂z be found (if the surface is F) by taking (∂F/∂z)/(∂F/∂x)? If that is allowed though I get (z+y)/x and when I differentiate with respect to time I still get a ∂y/∂t which I am not given a value for.
     
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