Calculus 3 : Directional Derivatives

Study concepts, example questions & explanations for Calculus 3

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Example Questions

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Example Question #1 : Directional Derivatives

Calculate , where  in the direction of .

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Correct answer:

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 .

Possible Answers:

Correct answer:

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 #3 : Directional Derivatives

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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 #9 : Directional Derivatives

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Example Question #10 : Directional Derivatives

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