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Differentiation and Chain Rule Concepts

Differentiation and Chain Rule Concepts

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
HSF.BF.B.3, HSF-BF.A.1C, HSF.TF.A.4

Standards-aligned

Created by

Amelia Wright

FREE Resource

Standards-aligned

CCSS.HSF.BF.B.3
,
CCSS.HSF-BF.A.1C
,
CCSS.HSF.TF.A.4
This video tutorial covers the chain rule of differentiation, focusing on finding derivatives of composite functions involving trigonometric functions. It provides a step-by-step guide on applying the chain rule, with examples including derivatives of functions like H(x) = 3cos(2x^3), G(x) = 9sec(4x+5), and others. Each example demonstrates identifying the inner and outer functions, calculating derivatives, and simplifying results.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the chain rule used for in differentiation?

Finding the derivative of a composite function

Finding the limit of a function

Finding the derivative of a single function

Finding the integral of a function

Tags

CCSS.HSF-BF.A.1C

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the function H(x) = 3 cos(2x^3), what is the inner function?

3x^2

cos(2x^3)

2x^3

3 cos(x)

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the inner function 2x^3 in the first example?

6x^2

3x^2

2x^2

6x

Tags

CCSS.HSF.TF.A.4

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the function G(x) = 9 sec(4x + 5), what is the derivative of the inner function 4x + 5?

5

4

9

1

Tags

CCSS.HSF.BF.B.3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the outer function in the example G(x) = 9 sec(4x + 5)?

sec(x)

9x

4x + 5

tangent(x)

Tags

CCSS.HSF.TF.A.4

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the function H(x) = 5 cos^3(x), what does the expression 'cos^3(x)' mean?

cos(x) plus 3

cos(x) raised to the power of 3

3 times cos(x)

cos(x) divided by 3

Tags

CCSS.HSF.BF.B.3

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of the inner function cos(x) in the third example?

-cos(x)

-sin(x)

cos(x)

sin(x)

Tags

CCSS.HSF.BF.B.3

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