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Homework Help: Computing ∂f/∂x (0,0)

  1. May 4, 2010 #1
    1. The problem statement, all variables and given/known data

    This is problem 2(a) from my midterm review sheet, found here: http://www.math.washington.edu/~sullivan/326smt_sp10.pdf

    2. Relevant equations

    Not sure what exactly I need here

    3. The attempt at a solution

    By the quotient rule, ∂f/∂x = [(x2+y2)(y2)-(xy2)(2x)]/[x2+y2]2. Obviously I can't just plug in (0,0). I thought about computing lim(x,y)-->(0,0) f(x,y), but the limit does exist, and doing that seems to be saved for part (b). Is there some theorem I should use to compute ∂f/∂x|(0,0)?

    Thank you for for help.
  2. jcsd
  3. May 4, 2010 #2
    OH! I think I might be on to something. I could first evaluate ∂f/∂x|x=0 , and then (∂f/∂x|x=0)|y=0.

    ∂f/∂x|x=0 = y4/y4 = 1 ---> (∂f/∂x|x=0)|y=0 = 1.

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