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Derivatives and Logarithmic Functions

Derivatives and Logarithmic Functions

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
HSF.BF.B.5, HSF-BF.A.1C

Standards-aligned

Created by

Liam Anderson

FREE Resource

Standards-aligned

CCSS.HSF.BF.B.5
,
CCSS.HSF-BF.A.1C
The video tutorial explains how to find the derivative of the function 3 log base 2 of (2x^2 - 3). It begins by introducing the concept of derivatives and the need to apply the chain rule. The inner function is identified as 2x^2 - 3, and its derivative is calculated. Since the logarithm's base is not e, a specific derivative formula is used. The tutorial walks through the steps of applying this formula, simplifying the expression, and arriving at the final derivative: 12x divided by the product of the natural log of 2 and (2x^2 - 3).

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5 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What rule is necessary to apply when finding the derivative of 3 log base 2 of the quantity 2x^2 - 3?

Product Rule

Power Rule

Chain Rule

Quotient Rule

Tags

CCSS.HSF-BF.A.1C

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the inner function U in the expression 3 log base 2 of the quantity 2x^2 - 3?

2x^2 - 3

2x^2 + 3

x^2 - 3

3x^2 - 2

Tags

CCSS.HSF.BF.B.5

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the inner function U, denoted as U Prime?

2x

4x

6x

8x

Tags

CCSS.HSF.BF.B.5

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which logarithmic base is used in the function 3 log base 2 of U?

Base 5

Base e

Base 10

Base 2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final expression for the derivative of 3 log base 2 of the quantity 2x^2 - 3?

6x / (ln 10 * (2x^2 - 3))

12x / (ln 10 * (2x^2 - 3))

6x / (ln 2 * (2x^2 - 3))

12x / (ln 2 * (2x^2 - 3))

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