Recent Lessons

Show all results for ""

Feature Overview

Ace your exams with our all-in-one platform for creating and sharing quizzes and tests.

Quizzes

Create quizzes and tests automatically from your content using AI.

Flashcards

Automatically turn your notes into digital flashcards.

Share, Export & Embed

Share with classmates or export to Excel and your learning management system.

Stats & Reporting

Auto-grading quizzes and tests with detailed stats and reports.

Mobile Apps

The smarter way to study – wherever you are.

Pricing

Search...

6 Questions

9 Views

Differentiation Formulas Quiz

Choose a study mode

Play Quiz

Study Flashcards

Spaced Repetition

Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the differentiation formula for the function f(x) = x^3 + 2x^2 - 5x + 3?

f'(x) = 3x^2 + 4x

f'(x) = 3x^2 + 2x

f'(x) = 3x^2 + 2x - 5

f'(x) = 3x^2 + 4x - 5 (correct)

What is the differentiation formula for the function g(x) = √(2x + 1)?

g'(x) = 1/√(2x)

g'(x) = √(2x + 1)

g'(x) = 1/√(2x + 1) (correct)

g'(x) = 1/2√(2x + 1)

What is the differentiation formula for the function h(x) = e^(2x)?

h'(x) = 2e^(2x) + C

h'(x) = 2e^(2x) (correct)

h'(x) = e^(2x) + C

h'(x) = e^(2x)

What is the integration formula for the function h(x) = e^(2x)?

∫ e^(2x) dx = (1/2)e^(2x) + C Signup and view all the answers

What is the integration formula for the function g(x) = √(2x + 1)?

∫ √(2x + 1) dx = (1/4)(2x + 1)^(3/2) + C Signup and view all the answers

What is the integration formula for the function f(x) = x^3 + 2x^2 - 5x + 3?

∫ (x^3 + 2x^2 - 5x + 3) dx = (1/4)x^4 + (2/3)x^3 - (5/2)x^2 + 3x + C Signup and view all the answers

Study Notes

Differentiation Formulas

For the function f(x) = x^3 + 2x^2 - 5x + 3, the differentiation formula is f'(x) = 3x^2 + 4x - 5.
For the function g(x) = √(2x + 1), the differentiation formula is g'(x) = 1 / (√(2x + 1)) * 2/2.
For the function h(x) = e^(2x), the differentiation formula is h'(x) = 2e^(2x).

Integration Formulas

For the function h(x) = e^(2x), the integration formula is ∫h(x)dx = (1/2)e^(2x) + C.
For the function g(x) = √(2x + 1), the integration formula is ∫g(x)dx = (2/3)(2x + 1)^(3/2) + C.
For the function f(x) = x^3 + 2x^2 - 5x + 3, the integration formula is ∫f(x)dx = (1/4)x^4 + (2/3)x^3 - (5/2)x^2 + 3x + C.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your knowledge of differentiation by finding the differentiation formulas for specific functions such as polynomial, square root, and exponential functions.