1. Directional Derivatives and Gradients
13.6

2. The first two slides contain the definitions and theorems that we need from 13.6 to work the exercises that follow.

3. The focus of this lesson is the directional derivative
The focus of this lesson is the directional derivative. We use this derivative to find the slope at a point on a surface in a specified direction. Check out the graphics on the first page of 13.6 in the text.
Through the gradient, we can use partial derivatives to find the directional derivative.

4. Example 1. Find the directional derivative of at
P(-1, 5) in the direction of
Solution: Find
Note in this example that

5. Example 2. Find the directional derivative of
at P(-5,-2) in the direction of
Solution. First find the unit vector in the direction of v.
Since

6. Example 3. Find the directional derivative of
at P(1,1,1) in the direction of
Solution.

7. Example 4. Find the directional derivative of in the direction of
Solution.

8. The following links will take you to presentations on Directional Derivatives and Gradients done at other colleges.
(Directional Derivatives are covered in the Part 2 tab.)
Oregon State
(This site is created by the people who make Mathematica software.)
(This is done at MIT. You HAVE to check this out just for the graphics.
Click on the link to get related text.)