Chapter 14 - Partial Derivatives - 14.6 Directional Derivatives and the Gradient Vector - 14.6 Exercises - Page 997: 8

a)$\nabla f=\biggl<2x\ln y, \dfrac{x^2}{y}\biggr>$ b)$\nabla f(3, 1)=\bigl<0, 9\bigr>$ c)$\dfrac{108}{13}$

a)$\nabla f=\biggl<2x\ln y, \dfrac{x^2}{y}\biggr>$ b)$\nabla f(3, 1)=\bigl<0, 9\bigr>$ c)$\mathbf{D_u}f(3, 1)=\nabla f(3, 1)\cdot \mathbf{u}=0+\dfrac{108}{13}=\dfrac{108}{13}$