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

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

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

Do I just use:

\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).