Question: Let \(f\left( x,y \right)=\frac{x+y}{xy}\)

(a) Find \(\nabla f\)

(b) Find the directional derivative of f at (1, 1), in the direction of (-1, 2).

(c) If \(z=\frac{x+y}{xy}\) and \(x={{u}^{2}}v\) and \(y={{e}^{uv}}\), find \(\frac{\partial z}{\partial v}\).