Answer
$$\nabla f\left( {x,y} \right) = - \frac{1}{3}{\bf{i}} - \frac{1}{2}{\bf{j}}$$
Work Step by Step
$$\eqalign{
& f\left( {x,y} \right) = 3 - \frac{x}{3} - \frac{y}{2} \cr
& {\text{Find the partial derivatives }}{f_x}\left( {x,y} \right){\text{ and }}{f_y}\left( {x,y} \right) \cr
& {f_x}\left( {x,y} \right) = \frac{\partial }{{\partial x}}\left[ {3 - \frac{x}{3} - \frac{y}{2}} \right] = - \frac{1}{3} \cr
& and \cr
& {f_y}\left( {x,y} \right) = \frac{\partial }{{\partial y}}\left[ {3 - \frac{x}{3} - \frac{y}{2}} \right] = - \frac{1}{2} \cr
& {\text{Calculate }}\nabla f\left( {x,y} \right) \cr
& \nabla f\left( {x,y} \right) = {f_x}\left( {x,y} \right){\bf{i}} + {f_y}\left( {x,y} \right){\bf{j}} \cr
& \nabla f\left( {x,y} \right) = - \frac{1}{3}{\bf{i}} - \frac{1}{2}{\bf{j}} \cr} $$
