## $f(x,y) = \begin{cases} \frac{xy^2}{x^2+y^2} \quad \text{if} \ (x,y)\not=(0,0)\\ 0 \quad \text{if} \ (x,y)=(0,0)\end{cases}$ differentiable?

$$f(x,y) = \begin{cases} \frac{xy^2}{x^2+y^2} \quad \text{if} \ (x,y)\not=(0,0)\ 0 \quad \text{if} \ (x,y)=(0,0)\end{cases}$$

Is this two-variable function differentiable at (0,0)?