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r.a.c.
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Homework Statement
We have [tex]f(x,y) = \frac{xy}{x^2+y^2}[/tex]
Show that the first partial derivative w.r.t. x and w.r.t y exist
Homework 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
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