Differentiation and Logarithmic Functions

Differentiation and Logarithmic Functions

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

Created by

Lucas Foster

FREE Resource

The video tutorial explains how to find the derivative of the function f(x) = x^3 sin(x) using logarithmic differentiation. It begins by substituting f(x) with y and taking the natural log of both sides. The tutorial then applies logarithmic properties to simplify the function and proceeds to differentiate both sides using the chain and product rules. Finally, it solves for the derivative, expressing it in terms of x, and presents the final derivative function.

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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial function given in the problem?

f(x) = x^3 * cos(x)

f(x) = x^2 * sin(x)

f(x) = x^3 * sin(x)

f(x) = x^3 + sin(x)

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What substitution is made for f(x) in the beginning?

f(x) is replaced with u

f(x) is replaced with y

f(x) is replaced with z

f(x) is replaced with v

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which property of logarithms is used to expand the right side of the equation?

Quotient property

Change of base property

Product property

Power property

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What rule is applied to differentiate the left side of the equation?

Power rule

Chain rule

Product rule

Quotient rule

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What additional factor appears when differentiating ln(y) with respect to x?

d^2x/dy^2

d^2y/dx^2

dx/dy

dy/dx

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which rule is used to differentiate the right side of the equation?

Quotient rule

Chain rule

Power rule

Product rule

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

x

ln(x)

1/x

x^2

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