Answer
$\dfrac{-11}{25\sqrt{34}}$
Work Step by Step
Formula to calculate the directional derivative: $D_uf=\nabla f(x,y) \cdot
u$
or, $D_uf=\nabla f(x,y) \cdot \dfrac{v}{|v|}$
This implies
At $(1,2)$
$D_uf (1,2)=\dfrac{3}{25} \times \dfrac{3}{\sqrt{34}}+\dfrac{-4}{25} \times \dfrac{5}{\sqrt{34}}$
Hence, $D_uf (1,2)=\dfrac{-11}{25\sqrt{34}}$
