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Logarithmic Differentiation and Trigonometric Identities

Logarithmic Differentiation and Trigonometric Identities

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
7.EE.A.1

Standards-aligned

Created by

Lucas Foster

FREE Resource

Standards-aligned

CCSS.7.EE.A.1
The video tutorial explains how to find the derivative of a function using logarithmic differentiation. The function involves a cosine term raised to a power that is also a function of x. The process involves taking the natural log of both sides, applying the chain and product rules, and simplifying the expression using trigonometric identities. The final derivative is expressed in terms of x.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is logarithmic differentiation used in this problem?

Because the exponent is a constant.

Because the exponent is a function of x.

Because the base is a constant.

Because the base is a function of x.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in applying logarithmic differentiation?

Using the chain rule.

Using the product rule.

Replacing f(x) with y.

Taking the derivative directly.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which property of logarithms is used to simplify the expression?

Change of base property

Power property

Quotient property

Product property

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What rule is applied to differentiate the natural log of a function?

Power rule

Quotient rule

Product rule

Chain rule

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of natural log u with respect to x?

1/u times u'

u times u'

1/u

u'

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the expression simplified after applying the product rule?

By using trigonometric identities

By factoring out common terms

By combining like terms

By expanding the expression

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What trigonometric identity is used to simplify the expression?

Cotangent

Sine

Cosine

Tangent

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