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?
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?
The only You have to do is to apply the definitions...
$\displaystyle \displaystyle \frac{\partial f(x,y)}{\partial x}= \lim_{h \rightarrow 0} \frac{f(x+h,y) - f(x,y)}{h}$
$\displaystyle \displaystyle \frac{\partial f(x,y)}{\partial y}= \lim_{h \rightarrow 0} \frac{f(x,y+h) - f(x,y)}{h}$
... for $\displaystyle f(x,y)= \sqrt{|x\ y|}$ ...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$