If I have a function $\displaystyle f(x,y)$ and I want to compute the directional derivative $\displaystyle \frac{\partial f}{\partial \bf{v}}(1,1)$ where $\displaystyle \bf{v}$ $\displaystyle =(1, -1)$

Then I use $\displaystyle \triangledown f(1,1) \cdot \frac{\bf{v}}{|\bf{v} |}$

But what if I want to find $\displaystyle \frac{\partial^2 f}{\partial \bf{v}}(1,1)$ ?

Do I just use:

$\displaystyle \langle f_{xx}, f_{yy} \rangle \cdot \frac{\bf{v}}{|\bf{v}|}$ ?

(I can find these questions in my exams, but I can't find them in my notes).