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Compute these partial derivatives with u = u(x,y), v = v(x,y); (x,y) = (1,1) = (u,v).

  1. Aug 2, 2012 #1

    s3a

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    1. The problem statement, all variables and given/known data
    The equations xu^2 + yv = 2, 2yv^2 + xu = 3 define u(x,y) and v(x,y) in terms of x and y near the point (x,y) = (1,1) and (u,v) = (1,1).

    Compute the following partial derivatives:
    (A) ∂u/∂x(1,1)
    (B) ∂u/∂y(1,1)
    (C) ∂v/∂x(1,1)
    (D) ∂v/∂y(1,1)

    The answers are:
    (A) ∂u/∂x(1,1) = -0.428571428571429
    (B) ∂u/∂y(1,1) = -0.285714285714286
    (C) ∂v/∂x(1,1) = -0.142857142857143
    (D) ∂v/∂y(1,1) = -0.428571428571429

    2. Relevant equations
    To my knowledge: partial differentiation and implicit differentiation.

    3. The attempt at a solution
    I tried implicitly and partially differentiating xu^2 + yv = 2 and got:
    u^2 + 2xu∂u/∂x = 0
    ∂u/∂x = -u^2 /(2xu)
    ∂u/∂x(1,1) = -(1)^2/(2*1*1) = -1/2 (which is close to the answer but not good enough).

    Could someone please tell me what I am doing wrong and how to do this correctly?

    Any help would be greatly appreciated!
    Thanks in advance!
     
  2. jcsd
  3. Aug 2, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    Re: Compute these partial derivatives with u = u(x,y), v = v(x,y); (x,y) = (1,1) = (u

    Where is the ∂v/∂x term in your partial derivative? You'll need to differentiate both equations with respect to both x and y and then treat it as a system of linear equations in the four unknowns.
     
  4. Aug 4, 2012 #3

    s3a

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    Re: Compute these partial derivatives with u = u(x,y), v = v(x,y); (x,y) = (1,1) = (u

    Your advice worked for me. Thanks!
     
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