Calculus 3 : Directional Derivatives

Example Questions

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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:

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