- #1

Telemachus

- 835

- 30

## Homework Statement

Well, I'm not sure about this one. Its actually a differentiation problem, it asks me to determine if the function is differentiable at the given point.

[tex]\sqrt[ ]{|xy|}[/tex] at [tex]P(0,0)[/tex]

I think its not, but I must demonstrate, off course.

So I try to solve the partial derivatives:

[tex]f_x=\begin{Bmatrix} \displaystyle\frac{|y|}{2\sqrt[ ]{|xy|}} & \mbox{ if }& x>0\\\displaystyle\frac{-|y|}{2\sqrt[ ]{|xy|}} & \mbox{if}& x<0\end{matrix}[/tex]

And here is the deal. Is this right? if it is, its easy to see that the partial derivative is not continuous at (0,0), its actually not defined at that point. So its not differentiable.

Bye there, and thanks.