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Derivatives and Chain Rule Concepts

Derivatives and Chain Rule Concepts

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
HSF.BF.B.3, HSF.IF.A.1, HSF-BF.A.1C

Standards-aligned

Created by

Lucas Foster

FREE Resource

Standards-aligned

CCSS.HSF.BF.B.3
,
CCSS.HSF.IF.A.1
,
CCSS.HSF-BF.A.1C
The video tutorial explains how to find the derivative of composite functions using the chain rule. It provides two examples: one with f(x) = sin(2ln(x)) and another with g(x) = cos(-3ln(x)). The process involves identifying the inner function, calculating its derivative, and applying the chain rule to find the derivative of the entire function. The tutorial concludes with a summary of the steps and encourages viewers to apply these techniques to similar problems.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in finding the derivative of a composite function?

Identify the outer function

Identify the inner function

Differentiate the outer function

Differentiate the inner function

Tags

CCSS.HSF-BF.A.1C

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the function f(x) = sin(2 ln(x)), what is the inner function?

x

2 ln(x)

cos(x)

sin(x)

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of 2 ln(x) with respect to x?

ln(x)

2/x

1/x

2x

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you express the derivative of f(x) = sin(2 ln(x)) using the chain rule?

sin(2 ln(x)) * x

sin(2 ln(x)) * 2/x

cos(2 ln(x)) * 2/x

cos(2 ln(x)) * x

Tags

CCSS.HSF.BF.B.3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified form of f'(x) for f(x) = sin(2 ln(x))?

2 cos(2 ln(x))/x

sin(2 ln(x))/x

cos(2 ln(x))/x

2 sin(2 ln(x))/x

Tags

CCSS.HSF.BF.B.3

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the function g(x) = cos(-3 ln(x)), what is the inner function?

sin(x)

x

-3 ln(x)

cos(x)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of -3 ln(x) with respect to x?

3/x

-3/x

-ln(x)

3 ln(x)

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