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Problem

Find the derivative of the function $ F(x) = \…

06:35

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Problem 1 Easy Difficulty

Find the derivative of $ f(x) = (1 + 2x^2)(x - x^2) $ in two ways: by using the Product Rule and by performing the multiplication first. Do your answer agree?


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01:47

Frank Lin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Related Topics

Derivatives

Differentiation

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Top Calculus 1 / AB Educators
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Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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Video Transcript

it's clear. So when you right here, So we're first going to use the product roll we get one plus two x square derivative X minus X square, plus one plus two X square times the derivative of X minus X square. Then we get zero plus four x times X minus X square plus one plus two X square times one minus two x We simplify. Let me go! Negative B X cube plus six X square minus two X plus one. Now we're gonna differentiate by multiplying everything out and then differentiating them separately. So we get X minus X square plus two x cubed minus two X plus two X cubed minus two x to the fourth. We do d y over DX, then we get negative eight x cubed Last six X square minus two x plus one

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Calculus: Early Transcendentals

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Related Topics

Derivatives

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Top Calculus 1 / AB Educators
Anna Marie Vagnozzi

Campbell University

Heather Zimmers

Oregon State University

Kayleah Tsai

Harvey Mudd College

Kristen Karbon

University of Michigan - Ann Arbor

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
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