# Calculus 3 : Directional Derivatives

## Example Questions

← Previous 1 3 4 5 6 7 8 9 35 36

### Example Question #1 : Directional Derivatives

Calculate , where  in the direction of .

Explanation:

The first thing to check is to see if the direction vector is a unit vector.

In order to see if it is a unit vector, we need to take the magnitude and see if it is equal to .

Now we are going to take partial derivatives in respect to , and then , and then multiply each partial by the component of the unit vector that corresponds to it.

The formula is:

### Example Question #2 : Directional Derivatives

Calculate , where  in the direction of .

Explanation:

The first thing to check is to see if the direction vector is a unit vector.

In order to see if it is a unit vector, we need to take the magnitude and see if it is equal to .

Now we are going to take partial derivatives in respect to , and then , and then multiply each partial by the component of the unit vector that corresponds to it.

The formula is:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation: