### All Calculus 3 Resources

## Example Questions

### Example Question #1 : Directional Derivatives

Calculate , where in the direction of .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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 #3 : Directional Derivatives

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**Correct answer:**

### Example Question #4 : Directional Derivatives

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### Example Question #5 : Directional Derivatives

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### Example Question #6 : Directional Derivatives

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### Example Question #7 : Directional Derivatives

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### Example Question #8 : Directional Derivatives

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### Example Question #1 : Directional Derivatives

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### Example Question #10 : Directional Derivatives

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