(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the definition of partial deriviatives as limits to findf_{x}(x,y) andf_{y}(x,y).

2. Relevant equations

f(x,y) = [tex]\frac{x}{x + y^{2}}[/tex]

3. The attempt at a solution

I don't think this is right because I think I should have an answer of 1.

f_{x}(x,y) = lim h-> 0 [f(x+h,y) - f(x,y)]/h

=lim h->0 [(x+h)/(x+h+y^2) - x/(x+y^2)]/h

=lim h->0 [(x+h)/(x+h+y^2) - x/(x+y^2)]*1/h

=lim h->0 (x+h)/(xh+h^2+(y^2)h) - x/(xh+(y^2)h)

=lim h->0 ((x/h)+1)/(x+h+y^2) - (x/h)/(x+y^2)

=1/(x+y^2)

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# Homework Help: Partial Derivatives

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