Answer
a)$\nabla f=\biggl<\dfrac{1}{y}, -\dfrac{x}{y^2}\biggr>$
b)$\nabla f(2, 1)=\bigl<1. -2\bigr>$
c)$-1$
Work Step by Step
For (a)
$\nabla f=\biggl<\dfrac{1}{y}, -\dfrac{x}{y^2}\biggr>$
For (b)
$\nabla f(2, 1)=\bigl<1. -2\bigr>$
For (c)
$\mathbf{D_u}f=\nabla f(2, 1)\cdot \mathbf{u}=\dfrac{3}{5}-\dfrac{8}{5}=-1$