Answer
$-\dfrac{4}{5}$
Work Step by Step
Our aim is to determine the directional derivative. In order to find it we have to use the expression:
$D_uf(x,y)=f_x(x,y)m+f_y(x,y)n$
Given: $f(x,y)=x^2e^{-y}; (-2,0)$ and in the direction towards the point $(2,-3)$
$D_uf(x,y)=2xe^{-y}\dfrac{4}{5}-x^2e^{-y}\dfrac{-3}{5}$
This implies:
From the given data, we have : $(x,y)=$ $(-2,0)$
$D_uf(0,1)=2(-2)e^{0}\dfrac{4}{5}-(-2)^2e^{0}\dfrac{-3}{5}=-\dfrac{4}{5}$
