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Multivariable Calculus Homework Help Please

  1. Apr 1, 2014 #1
    1. The problem statement, all variables and given/known data

    See in picture

    2. Relevant equations

    What is the final answer?

    3. The attempt at a solution

    I know dw/du = df/dx * dx/du + df/dy * dy/du

    & that dx/du = -8sinu & dy/du = -4sinvsinu

    Stumped on how to get df/dx and df/dy
     

    Attached Files:

  2. jcsd
  3. Apr 1, 2014 #2

    Mark44

    Staff: Mentor

    It seems odd to me that the question is asking for wu(##\pi/2, 0##) when the partials they give you are evaluated at (0, 0). Unless there's something I'm not thinking of, I would say that there is a typo in the problem.
     
  4. Apr 1, 2014 #3
    nope, I asked my prof because I was confused too, but he said that is how it is.
     
  5. Apr 1, 2014 #4
    I thought the same until I got my head screwed on straight and realized ##w_u(\pi/2, 0)=w_u|_{(u,v)=(\pi/2, 0)}## and that ##x(\pi/2, 0)=y(\pi/2, 0)=0##.

    So the more "complete" form of the chain rule that applies here is $$w_u(u,v)=\frac{\partial f}{\partial x}\Big(x(u,v),y(u,v)\Big)\frac{\partial x}{\partial u}(u,v)+\frac{\partial f}{\partial y}\Big(x(u,v),y(u,v)\Big)\frac{\partial y}{\partial u}(u,v)$$ or $$w_u(u,v)=f_x\Big(x(u,v),y(u,v)\Big)x_u(u,v)+f_y\Big(x(u,v),y(u,v)\Big)y_u(u,v)$$
     
    Last edited: Apr 1, 2014
  6. Apr 1, 2014 #5
    But the final answer is supposed to be a number, wouldn't this give me a answer in coordinates?
     
  7. Apr 1, 2014 #6
    What would you get if you plugged in ##\pi/2## for ##u## and ##0## for ##v##?
     
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