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Derivatives of Exponential and Logarithmic Functions

Derivatives of Exponential and Logarithmic Functions

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

Created by

Ethan Morris

FREE Resource

The video tutorial explains how to find derivatives of functions using logarithmic differentiation. It provides a formula for derivatives of the form U^V and demonstrates its application through various examples, including x^x, x^sin(x), ln(x)^x, x^ln(x), x^e^x, and sin(x)^x. The video also mentions additional resources and formula sheets available in the description.

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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 x raised to the x using logarithmic differentiation?

Apply the power rule

Use the product rule

Use logarithmic differentiation

Differentiate directly

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the formula for the derivative of u raised to the v, what does 'v u prime' represent?

The quotient of v and u

The product of v and the derivative of u

The derivative of v with respect to u

The sum of v and u

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

When finding the derivative of x raised to the sin x, what is the derivative of sin x?

1

x

sin x

cos x

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the simplified form of the derivative of ln x raised to the x?

x times ln x

x raised to ln x times ln x

ln x raised to x times 1/ln x plus ln ln x

ln x times x

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the derivative of x raised to ln x, what is the expression for v prime?

1

x

ln x

1/x

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final simplified form of the derivative of x raised to ln x?

x raised to ln x times ln x

x raised to ln x times 2 ln x over x

ln x times x

x times ln x

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of e^x with respect to x?

e^x

1

x

ln x

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