### All Calculus 3 Resources

## Example Questions

### Example Question #1 : Multi Variable Chain Rule

Compute for , , .

**Possible Answers:**

**Correct answer:**

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:**

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:**

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:**

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:**

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:**

The chain rule states .

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

In this problem

### Example Question #7 : Multi Variable Chain Rule

Use the chain rule to find when , , .

**Possible Answers:**

**Correct answer:**

The chain rule states .

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

In this problem

### Example Question #8 : Multi Variable Chain Rule

Use the chain rule to find when , , .

**Possible Answers:**

**Correct answer:**

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:**

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:**

The chain rule states .

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

In this problem,

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