I'm stuck on the following problem in my preparation for an upcoming exam:
Suppose $f(x,y)$ is a continuously differentiable function on $\mathbb{R}^2$. It is known that the directional derivatives satisfy $D_\textbf{u} f(0,0)<\frac{\partial f}{\partial x}=2$ for all $\textbf{u}\neq \textbf{i}$. Find $\frac{\partial f}{\partial y}(0,0)$.
I would just appreciate a hint that can help me solve the problem. Thank you in advance