# Parcial derivation of two variable function

1. Oct 22, 2012

### Jalo

1. The problem statement, all variables and given/known data

Given the function f(x) defined as:

(x^3-y^3)/(x^2+y^2) if (x,y)≠(0,0)
0 if (x,y)=(0,0)

Find the parcial derivatives of the function at the point (0,0).
Is the function f differentiable?

2. Relevant equations

3. The attempt at a solution

d/dx [ (x^3-y^3)/(x^2+y^2)] = [3x^2(x^2+y^2) - 2x(x^3-y^3)] / (x^2+y^2)^2 =
= [x^4+3x^2*y^2+2xy^3]/(x^4+2x^2y^2+y^4)

I can't find the way out of this indetermination... As to the second question, if the parcial derivatives exist then the function is differentiable in the point (0,0).
I know from the solutions that the result will be 1 and -1.

If anyone could point me in the right direction I'd really appreciate!

Thanks!

2. Oct 22, 2012

### tiny-tim

Hi Jalo!

(try using the X2 button just above the Reply box )

∂/∂x means the derivative keeping y fixed

so ∂/∂x at (0,0), or at (anything,0) is the derivative keeping y = 0

(and ∂/∂y at (0,0) is the derivative keeping x = 0 )

sooo … ?

3. Oct 22, 2012

### Jalo

Oh lol... I can't believe I didn't saw that!
I was thinking as if it both x and y were tending to 0... I guess I'm spending too much time solving limits!

Thanks!