Answer
$\dfrac{7\sqrt{5}}{10}$
Work Step by Step
$\nabla f=\biggl<\sqrt{t}, \dfrac{s}{2\sqrt{t}}\biggr>$
$\hat{v}=\biggl<\dfrac{2}{\sqrt{5}}, -\dfrac{1}{\sqrt{5}}\biggr>$
Then,
$\nabla f_{(2, 4)}=\biggl<2, \dfrac{1}{2}\biggr>$
Therefore,
$\mathbf{D_\hat{v}}f_{(2, 4)}=\nabla f_{(2, 4)}\cdot\hat{v}=\dfrac{4}{\sqrt{5}} -\dfrac{1}{2\sqrt{5}}=\dfrac{7\sqrt{5}}{10}$
