# Multivariable Calculus : Partial Differentiation

## Example Questions

### Example Question #1 : Differentiation Rules

Find .

Explanation:

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 .

Explanation:

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 .

Explanation:

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 .

Explanation:

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 .