Possible Duplicate:
Evaluate the partial derivatives of the following function:
The function $f:\mathbb R^2 \to \mathbb R$, defined as: $\left\{\begin{align*}&\frac{x^5y}{x^4+y^2}&&(x,y) \neq 0\\&0&&(x,y)=(0,0)\end{align*}\right.$ Using the limit definition I get:
$f_x(0,0) = \frac{(0+h)^2 (0)}{h(0+h)^4+(0)} - \frac{(0)^5(0)}{h(0)^4+h(0)^2}$
for both $f_x$ and $f_y$, I get $\frac00$ terms for the last term. I know that the answer to both is $0$, but how do I deal with the $\frac00$ term (I can't seem to get rid of it). Is this allowed?
Thanks for any insight!