I'm trying to solve this excercise: find all directional derivatives of the function $f(x,y)=2x+y-\pi^2$ at point $(0,0)$.
Now, I'm applying the definition so I calculate the limit($\alpha \ and \ \beta$ are the directions and $(x_0,y_0)=(0,0)$)
$\lim_{t\to 0} \frac{f(x_0+t\alpha , y_0+t\beta)-f(x_0,y_0)}{t} = \lim_{t\to 0} \frac{2t\alpha+t\beta-\pi^2+pi^2}{t} = \lim_{t\to 0} 2\alpha+\beta$
But now I don't know how to use this result to find all directional derivatives. Can someone explain me how can I proceed to find the result?