Partial Differentiation

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Multivariable Calculus › Partial Differentiation

Questions 1 - 10
1

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

2

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:

3

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:

4

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:

5

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

6

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:

7

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:

8

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:

9

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

10

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