1. The problem statement, all variables and given/known data What is the directional derivative of the function z = x3 - y at the point (1, 2, -1) and in the direction of a vector (1,1,1)? 2. Relevant equations 3. The attempt at a solution If f(x,y) = x3 - y, then ∇f = (3x2, -1) which equals (3, -1) at the given point. Now I understand I have to take the dot product of the gradient with the unit vector (1/√3, 1/√3, 1/√3) but I'm not quite sure how to... Can a function like z = f(x,y) have a directional derivative in the direction of a three dimensional vector? Thanks for any help!