Partial Derivatives and Chain Rule

Partial Derivatives and Chain Rule

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

Created by

Olivia Brooks

FREE Resource

The video tutorial explains how to find the partial derivative of the function 3xE^(3xy) with respect to x. It begins by treating y as a constant and differentiating with respect to x. The function is rewritten as F(x, y) = 3xE^(3xy), and the chain rule is applied, identifying the inner function U as 3xy. The derivative of U with respect to x is calculated as 3y. The partial derivative is then expressed as 9yE^(3xy), representing the slope of the tangent line in the x direction. The tutorial concludes with a brief application of the derivative.

Read more

6 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial function given for finding the partial derivative with respect to x?

3y * e^(3xy)

3x * e^(xy)

3x * e^(3xy)

3y * e^(xy)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When finding the partial derivative with respect to x, how is y treated?

As a constant

As a variable

As a function

As a derivative

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is identified as the inner function u when applying the chain rule?

3y

e^(3xy)

3xy

3x

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the inner function u = 3xy with respect to x?

3x

3

3y

xy

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified expression for the partial derivative with respect to x?

3y * e^(3xy)

9x * e^(3xy)

9y * e^(3xy)

3x * e^(3xy)

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the partial derivative with respect to x represent in terms of the function's graph?

The maximum point of the graph

The curvature of the graph

The slope of the tangent line in the x direction

The slope of the tangent line in the y direction

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Google

Continue with Google

Email

Continue with Email

Classlink

Continue with Classlink

Clever

Continue with Clever

or continue with

Microsoft

Microsoft

Apple

Apple

Others

Others

Already have an account?