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Functions of Two Variables. Need Help!

  1. May 20, 2007 #1
    I need some help with one of my tutorial questions. This is the question

    For Part (a), I have found the partial derivatives as

    Fx (x,y) = Cos(x) Sin(y)
    Fy (x,y) = Sin(x) Cos (y)

    Then to find the stationary points, Let Fx = 0 and Fy = 0. But im not sure how to find the values..

    For Part (b), I have no idea how to solve it..

    For Part (c), I know the chain rule for two variables but im not sure how to apply it to this question. If someone could point out an example that would be great =)

    Thx for the help!
  2. jcsd
  3. May 20, 2007 #2


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    Science Advisor
    Homework Helper

    (a)Fx = 0 when x = 0 or y = pi/2, or x = pi or y = 3pi/2 etc. as long as you are confined within the domain.

    (b) hint: gradient of function is the normal vector of the function surface at a certain point.

    chain rule is
    dg/dt = (df/dx)(dx/dt) + (df/dy)(dy/dt)

    were x = t^2; y = exp(t)

    if then f(x,y) is Sin(x) * Sin(y)

    we get:

    df/dx = Cos(t^2) Sin(exp(t))

    and (df/dx)*(dx/dt) = 2tCos(t^2) Sin(exp(t))

    similar for (df/dy)(dy/dt)

    but I am not so sure about the chain rule anymore.
    Last edited: May 20, 2007
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