Computing ∂f/∂x (0,0) | Midterm Review Sheet Problem 2(a)

[Jamin2112]

Homework Statement

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

Homework Equations

Not sure what exactly I need here

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.

 

[Jamin2112]

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?