Chapter 14 - Partial Derivatives - 14.6 Directional Derivatives and the Gradient Vector - 14.6 Exercises - Page 997: 14

$-\dfrac{18}{5}$

$\nabla g=\biggl<2ue^{-v}, -u^2e^{-v}\biggr>$ $\nabla g(3, 0)=\biggr<6, -9\biggr>$ $\hat{v}=\biggl<\dfrac{3}{5}, \dfrac{4}{5}\biggr>$ $\mathbf{D_u}g(3, 0)=\nabla g(3, 0)\cdot\hat{v}=\dfrac{18}{5}+\dfrac{-36}{5}=-\dfrac{18}{5}$