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...

Calculus 1 Basic Differentiation Rules: Sum and Difference Rules

10 Questions

2 Views

Calculus 1 Basic Differentiation Rules: Sum and Difference Rules

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 derivative of the function y = (1 + 2x^4) / (1 - 2x^4) using the Chain Rule?

(8x^3) / (1 - 2x^4)

(16x^3) / (1 - 2x^4)^2 (correct)

(8x^3) / (1 - 2x^4)^2

(16x^3) / (1 - 2x^4)

If f(x) = x^3 - 3 and g(x) = x^3 - 3, what is the derivative of f(g(x))?

200x^2(x^3 - 3)^99 * 3x^2

300x^2(x^3 - 3)^99 * 3x^2 (correct)

300x^2(x^3 - 3)^98 * 3x^2

300x^2(x^3 - 3)^99 * 2x

If f(x) = x^4 - 2x^3 + 2x - 11 and g(x) = x^4 - 2x^3 + 2x - 11, what is f'(g(x))?

(3x^3 - x^2 + 1) / (x^4 - x^3 + 2x)

(2x^3 - 3x^2 + 1) / (x^4 - 2x^3 + 2x) (correct)

(3x^3 - 3x^2 + 1) / (x^4 - 2x^3 + 2x)

(2x^3 - x^2 + 1) / (x^4 - x^3 + 2x)

For a function y = x^(5/2), what is its derivative?

(5/2)x^(3/2) Signup and view all the answers

Given y = √x * e^(2x), what is dy/dx?

(e^(2x) + 2√x * e^(2x)) / (2√x) Signup and view all the answers

What is the derivative of y = e^(3x) / x?

(e^(3x)(3 - x)) / x^2 Signup and view all the answers

If f(x) = ln(x), what is f'(x)?

(1/x) Signup and view all the answers

For y = cos(πx), what is dy/dx?

-πsin(πx) Signup and view all the answers

What is the derivative of y = tan(4π/x)?

-4πsec²(4π/x) Signup and view all the answers

If f(x) = e^(5cos(x)), what is f'(x)?

-5sin(x)e^(5cos(x)) Signup and view all the answers