# Thread: Theorem concerning partial differentiation

1. ## Theorem concerning partial differentiation

The question is:

Prove that
$\displaystyle f(x,y) = xy / (x^2+y^2)^2$ x,y are not zero
$\displaystyle f(0,0) = 0$

satisfies Laplace's equation $\displaystyle d^2f/dx^2 + d^2f/dy^2 = 0$ everywhere

And we are supposed to use the theorem which states that the function f is differentiable at (a,b) if f and its partials exist at each point of the neighborhood and continuous at (a,b)

No idea how to start this problem....

2. Originally Posted by geegee
The question is:

Prove that
$\displaystyle f(x,y) = xy / (x^2+y^2)^2$ x,y are not zero
$\displaystyle f(0,0) = 0$

satisfies Laplace's equation $\displaystyle d^2f/dx^2 + d^2f/dy^2 = 0$ everywhere

And we are supposed to use the theorem which states that the function f is differentiable at (a,b) if f and its partials exist at each point of the neighborhood and continuous at (a,b)

No idea how to start this problem....
Calculate $\displaystyle \frac{\partial^2 f}{\partial x^2}$ and $\displaystyle \frac{\partial^2 f}{\partial y^2}$ show that when you add them you get 0. It's really straight forward.