#### Answer

$\dfrac{327}{13}$

#### Work Step by Step

Our aim is to determine the direction derivative of $f(x,y)$.In order to find this, we have : $D_uf=|\nabla f(x,y)|$
or, $D_uf=\nabla f(x,y) \cdot u$
From the given data ion the question, we have $f_x(1,3)=3 , f_y(1,3)=26$
This implies
$D_uf=\nabla f(x,y) \cdot u$
or, $D_uf(1,3)=f_x(1,3)(\dfrac{5}{13})+f_y(1,3)(\dfrac{12}{13})$
Thus,$D_uf(1,3)=3(\dfrac{5}{13})+26(\dfrac{12}{13})$
$D_uf(1,3)=\dfrac{327}{13}$