Finding partial derivative of $f(x,y)=\frac{xy}{\sqrt{x^2+y^2}}$ I'm studying Mathematical Analysis II for a university course. There is a training exercise that asks me to:

Find the partial derivatives at $(1,0)$ of $f(x,y)$, where:
$f(x,y)=\frac{xy}{\sqrt{x^2+y^2}}$ when $(x,y)\neq (0,0)$ and
$f(x,y) = 0$ when $(x,y)= (0,0)$

So far, I've used the definition as per the other examples. For example, let's start with $f_x(a,b)=g'(a)=\lim_{h\to 0}\frac{f(a+h,b) - f(a,b)}{h}$
Applied to my problem, I've got $f_x(1,0)=\lim_{h\to 0}\frac{f(1+h,0) - f(1,0)}{h}$
And this is where I stall. According to other examples, this is supposed to equal $\frac{0}{h}=0$ , but HOW?
And then I'm supposed to get the limit to +inf?
Am I using the wrong methodology?

$f(1+h,0)=\frac{1+h. 0}{\sqrt{(1+h)^2+0^2}}=0$ similarly $f(1,0)=0$ thus $f_x(1,0)=\lim_{h\to 0}\frac{f(1+h,0) - f(1,0)}{h}=\lim_{h\to 0}\frac{0}{h}=0$
