# Thread: Is this Function C^2?

1. ## Is this Function C^2?

Hello,

given the following function from R^2 to R^2:

f(x,y)=1/(x^2+y^2) * (x,y) if (x,y) not (0,0)
f(x,y)=0 if (x,y)=(0,0)

Is that function C^2 (= 2 times continuously differentiable)?

A yes/no answer would be enough.

Regards,
engmaths

2. ## Re: Is this Function C^2?

Hey engmaths.

Do you need to differentiate it over the entire R^2 region? If you need to do this then you can show that you have a discontinuity and hence it is not differentiable.

If you exclude this point, then show that the function is differentiable (using the definition) and apply it again for the first derivative.