1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.

    Right?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook