Find the direction in which the maximum rate of change occurs for the function f(x,y) = 4xsin(xy) at the point (5,1) . Give your answer as a unit vector.
a) ⟨1, 0⟩
b) ⟨0, 1⟩
c) ⟨1/√2, 1/√2⟩
d) ⟨-1/√2, -1/√2⟩