### All Multivariable Calculus Resources

## Example Questions

### Example Question #1 : Differentiation Rules

Find .

**Possible Answers:**

**Correct answer:**

In order to find , we need to take the derivative of in respect to , and treat , and as constants. We also need to remember what the derivatives of natural log, exponential functions and power functions are for single variables.

Natural Log:

Exponential Functions:

Power Functions:

### Example Question #2 : Differentiation Rules

Find .

**Possible Answers:**

**Correct answer:**

In order to find , we need to take the derivative of in respect to , and treat , and as constants. We also need to remember what the derivatives of natural log, exponential functions and power functions are for single variables.

Natural Log:

Exponential Functions:

Power Functions:

### Example Question #3 : Differentiation Rules

Find .

**Possible Answers:**

**Correct answer:**

In order to find , we need to take the derivative of in respect to , and treat , and as constants. We also need to remember what the derivatives of natural log, exponential functions and power functions are for single variables.

Natural Log:

Exponential Functions:

Power Functions:

### Example Question #1 : Arc Length

Determine the length of the curve , on the interval .

**Possible Answers:**

**Correct answer:**

First we need to find the tangent vector, and find its magnitude.

Now we can set up our arc length integral

### Example Question #2 : Partial Differentiation

Determine the length of the curve , on the interval .

**Possible Answers:**

**Correct answer:**

First we need to find the tangent vector, and find its magnitude.

Now we can set up our arc length integral

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