# Math Help - Partial Derivative at the origin.

1. ## Partial Derivative at the origin.

Let f(x, y) = sqrt( abs(xy))

Verify that the x partial derivative and the y partial derivative are both 0 at the origin.

Once I take the partial derivative, I can't substitute (0, 0) because then I would get 0/0. How do I go around this problem?

2. The only You have to do is to apply the definitions...

$\displaystyle \frac{\partial f(x,y)}{\partial x}= \lim_{h \rightarrow 0} \frac{f(x+h,y) - f(x,y)}{h}$

$\displaystyle \frac{\partial f(x,y)}{\partial y}= \lim_{h \rightarrow 0} \frac{f(x,y+h) - f(x,y)}{h}$

... for $f(x,y)= \sqrt{|x\ y|}$ ...

Kind regards

$\chi$ $\sigma$