Understanding Derivatives of Natural Log Functions

Understanding Derivatives of Natural Log Functions

Assessment

Interactive Video

Mathematics

11th Grade - University

Hard

Created by

Amelia Wright

FREE Resource

The video tutorial explains how to find the derivative of a natural log function using the chain rule. It begins by simplifying the function using logarithm properties, then applies the chain rule to find the derivative. The process involves rewriting the function, applying the chain rule, simplifying the derivative, and combining fractions to reach the final derivative expression.

Read more

10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in finding the derivative of a natural log function in its current form?

Apply the product rule

Use integration by parts

Differentiate directly

Use the chain rule

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can the square root be rewritten to simplify the derivative process?

As a logarithm

As a rational exponent

As a polynomial

As a constant

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What property of logarithms allows us to express the function as a difference of two logs?

Product property

Power property

Quotient property

Change of base property

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the inner function 'U' when applying the chain rule to the natural log of 3X to the 4th + 2?

3X to the 4th + 2

4X

1/2

Natural log of 3X

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the natural log of a function U?

1/U squared

1/U times U prime

U prime times U

U squared

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of distributing the 1/2 in the expression before finding the derivative?

To change the base of the logarithm

To eliminate the logarithm

To make the function continuous

To simplify the expression

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the natural log of 4X?

Natural log of 4

1/2X

4X

1/4X times 4

Create a free account and access millions of resources

Create resources
Host any resource
Get auto-graded reports
or continue with
Microsoft
Apple
Others
By signing up, you agree to our Terms of Service & Privacy Policy
Already have an account?