# Very Easy Differential Question

1. Mar 12, 2010

### r.a.c.

1. The problem statement, all variables and given/known data
We have $$f(x,y) = \frac{xy}{x^2+y^2}$$
Show that the first partial derivative w.r.t. x and w.r.t y exist

2. Relevant equations

f(x+dx,y)-f(x,y) = a(dx) + o(dx) where a is some number and o(dx)(not o multiplied by dx rather a 'function', if so to say, o of dx) is such that o(dx)/dx goes to 0 as dx goes to 0

3. The attempt at a solution

I am stuck at the very beginning by just substituting for f(x+dx,y)-f(x,y) and then I don't know what to do. I am not able to tell which part is a(dx) and which part is o(dx). This is absurdly easy and I've done such things before but I am having a block and for some reason can't get past the algebra. Thanks