### All Calculus 3 Resources

## Example Questions

### Example Question #11 : Differentials

Find the differential of the function:

**Possible Answers:**

**Correct answer:**

The differential of the function is given by

To find the given partial derivative of the function, we must treat the other variable(s) as constants.

The partial derivatives are

### Example Question #1431 : Partial Derivatives

Find the differential of the function:

**Possible Answers:**

**Correct answer:**

The differential of a function is given by

The partial derivatives of the function are

### Example Question #12 : Differentials

Find the differential of the function:

**Possible Answers:**

**Correct answer:**

The differential of the function is given by

The partial derivatives are

### Example Question #12 : Differentials

Find the total differential, , of the following function

**Possible Answers:**

**Correct answer:**

The total differential is defined as

For the function

We first find

by taking the derivative with respect to and treating as a constant.

We then find

by taking the derivative with respect to and treating as a constant.

We then substitute these partial derivatives into the first equation to get the total differential

### Example Question #13 : Differentials

Find the total differential, , of the following function

**Possible Answers:**

**Correct answer:**

The total differential is defined as

For the function

We first find

by taking the derivative with respect to and treating as a constant.

We then find

by taking the derivative with respect to and treating as a constant.

We then substitute these partial derivatives into the first equation to get the total differential

### Example Question #14 : Differentials

Find the total differential, , of the following function

**Possible Answers:**

**Correct answer:**

The total differential is defined as

For the function

We first find

by taking the derivative with respect to and treating as a constant.

We then find

by taking the derivative with respect to and treating as a constant.

We then substitute these partial derivatives into the first equation to get the total differential

### Example Question #15 : Differentials

If , calculate the differential when moving from to.

**Possible Answers:**

**Correct answer:**

The equation for is

.

Evaluating partial derivatives and substituting, we get

Plugging in, we get

.

### Example Question #16 : Differentials

If , calculate the differential when moving from the point to the point .

**Possible Answers:**

**Correct answer:**

The equation for is

.

Evaluating partial derivatives and substituting, we get

Plugging in, we get

.

### Example Question #17 : Differentials

If , calculate the differential when moving from the point to the point .

**Possible Answers:**

**Correct answer:**

The equation for is

.

Evaluating partial derivatives and substituting, we get

Plugging in, we get

### Example Question #19 : Differentials

Find the differential of the following function:

**Possible Answers:**

**Correct answer:**

The differential of the function is given by

The partial derivatives are

, ,

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