Find the maximum rate of change of f(x,y)=?

Question

Answer 1

∂f/∂x = 2x / (x^2 + y^2)

∂f/∂x at (5, -1) = 10 / 26 = 5/13

∂f/∂y = 2y / (x^2 + y^2)

∂f/∂y at (5, -1) = -2 / 26 = -1/13

∇f(5, - 1) = (5/13)i - (1/13)j

Max Value = [(5/13)^2 + (-1/13)^2]^(1/2) = (2/13)^(1/2)

Unit Vector = (5/13)i / (2/13)^(1/2) - (1/13)j / (2/13)^(1/2)