Answer
$\approx 0.778$
Work Step by Step
Formula to calculate the directional derivative is:
$D_uf(x,y)=f_x(x,y)m+f_y(x,y)n$
From the given data, we have
$m=\dfrac{1}{\sqrt2}$ and $n=\dfrac{1}{\sqrt2}$
$D_uf(x,y)=\dfrac{-39-(-26))}{-25-(-15)} \times \dfrac{1}{\sqrt2}+\dfrac{-34-(-30))}{40-20} \times \dfrac{1}{\sqrt2}$
or,
$=(\dfrac{13}{10}) \times \dfrac{1}{\sqrt2}+(\dfrac{-1}{5}) \times \dfrac{1}{\sqrt2}$
or,
$\approx 0.778$
