- #1

KillerZ

- 116

- 0

## Homework Statement

Use the definition of partial deriviatives as limits to find

*f*

_{x}(x,y) and

*f*

_{y}(x,y).

## Homework Equations

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

## 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)