(Solved): Find the rate of change of the function \( f(x, y)=\sqrt{x^{2}+y^{2}} \) at the point \( (1,-2) \) ...

Find the rate of change of the function \( f(x, y)=\sqrt{x^{2}+y^{2}} \) at the point \( (1,-2) \) and in the direction of the vector \( (1,2) \), and also find a point at which the rate of change doesn't exist. \[ D_{(1,2)} f(1,-2)= \] \( f \) is NOT differentiable at the point