Let $f: \mathbb{R}^2 \to \mathbb{R} $ be given as 

$$
f(x,y) =
\begin{cases}
y, & \text{if }\text{ $x^2 = y $} \\
0, & \text{if }\text{ $x^2 \neq y $}
\end{cases}
$$

Is this function differentiable at $(0,0)$ ?