- #1

- 31

- 2

## Homework Statement

What is the directional derivative of the function z = x

^{3}- y at the point (1, 2, -1) and in the direction of a vector (1,1,1)?

## Homework Equations

## The Attempt at a Solution

If f(x,y) = x

^{3}- y, then ∇f = (3x

^{2}, -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!