Calculus 3 : Multi-Variable Chain Rule

Study concepts, example questions & explanations for Calculus 3

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1 3 4

Example Question #1 : Multi Variable Chain Rule

Compute  for .

Possible Answers:

Correct answer:

Explanation:

All we need to do is use the formula for multivariable chain rule.

When we put this all together, we get.

Example Question #2 : Multi Variable Chain Rule

Evaluate  in terms of  and/or  if ,  , and .

Possible Answers:

Correct answer:

Explanation:

Expand the equation for chain rule.

Evaluate each partial derivative.

,  

Substitute the terms in the equation.

Substitute .

The answer is:  

Example Question #3 : Multi Variable Chain Rule

Use the chain rule to find  when  .

Possible Answers:

Correct answer:

Explanation:

The chain rule states .

Since  and  are both functions of  must be found using the chain rule.

 

In this problem

Example Question #4 : Multi Variable Chain Rule

Use the chain rule to find  when  .

Possible Answers:

Correct answer:

Explanation:

The chain rule states .

Since  and  are both functions of  must be found using the chain rule.

 

In this problem

Example Question #5 : Multi Variable Chain Rule

Use the chain rule to find  when  .

Possible Answers:

Correct answer:

Explanation:

The chain rule states .

Since  and  are both functions of  must be found using the chain rule.

 

In this problem

 

 

Example Question #6 : Multi Variable Chain Rule

Use the chain rule to find  when  .

Possible Answers:

Correct answer:

Explanation:

 

 The chain rule states .

Since  and  are both functions of  must be found using the chain rule.

 

In this problem

 

Example Question #1 : Multi Variable Chain Rule

Use the chain rule to find  when  .

Possible Answers:

Correct answer:

Explanation:

 The chain rule states .

Since  and  are both functions of  must be found using the chain rule.

 

In this problem

 

Example Question #2 : Multi Variable Chain Rule

Use the chain rule to find  when  .

Possible Answers:

Correct answer:

Explanation:

The chain rule states .

Since  and  are both functions of  must be found using the chain rule.

 

In this problem

 

 

Example Question #9 : Multi Variable Chain Rule

Use the chain rule to find  when  .

Possible Answers:

Correct answer:

Explanation:

The chain rule states .

Since  and  are both functions of  must be found using the chain rule.

 

In this problem,

 

 

Example Question #10 : Multi Variable Chain Rule

Use the chain rule to find  when  .

Possible Answers:

Correct answer:

Explanation:

The chain rule states .

Since  and  are both functions of  must be found using the chain rule.

 

In this problem,

 

 

 

← Previous 1 3 4
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: