Find the directional derivative of the function at the given point in the direction of the vector v. f(x, y, z) = xe^y + ye^z + ze^x, (0, 0, 0), v = 6, 3, −3

Step-by-step explanation:

We need to find the directional derivative of the function at the given point in the direction of the vector v.

,point (0, 0, 0) and

By Theorem: If f is a differentiable function of x , y and z , then f has a directional derivative for any unit vector and

where

since,  

then

The partial derivatives are

Then the directional derivative is

so, directional derivative at point (0,0,0)

12/11c

or

12

c

11