Search Header Logo
Partial Derivatives and Their Applications

Partial Derivatives and Their Applications

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

Created by

Olivia Brooks

FREE Resource

The video tutorial explains how to find first and second order partial derivatives of a function with respect to x and y. It covers the process of treating one variable as a constant while differentiating with respect to the other. The tutorial also discusses mixed partial derivatives and their significance. Finally, it explains how the sign of second order partial derivatives indicates the concavity of the function in different directions.

Read more

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in finding second order partial derivatives?

Integrate the function with respect to X.

Calculate the second order derivatives directly.

Differentiate the function with respect to Y.

Find the first order partial derivatives.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When finding the partial derivative of a function with respect to X, what is treated as a constant?

Y

Neither X nor Y

Both X and Y

X

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of 5x^6 with respect to Y?

6x^5

5x^5

0

30x^5

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you find the second order partial derivative with respect to X?

Differentiate with respect to X and then Y.

Differentiate with respect to Y and then X.

Differentiate with respect to X twice.

Differentiate with respect to Y twice.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of differentiating 30x^5 with respect to X again?

150x^4

0

30x^4

150x^5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are mixed partial derivatives?

Derivatives taken with respect to different variables in sequence.

Derivatives taken with respect to the same variable twice.

Derivatives that are always zero.

Derivatives that do not exist.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the mixed partial derivative of 12x y^2 with respect to Y and then X?

0

24xy

12y^2

12x

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?