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Regard $ y $ as the independent variable and $ x …

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Problem 23 Easy Difficulty

Regard $ y $ as the independent variable and $ x $ as the dependent variable and use implicit differentiation to find $ dx/dy. $
$ x^4y^2 - x^3y +2xy^3 = 0 $


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01:35

Frank Lin

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

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Derivatives

Differentiation

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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

this problem or winning equation, whereas to find Derek off exits. Why? Since wise independent for your one exit. And so we're gonna think there was a lot of friends with respect. Why was to that organist for a group or the terms, actually, So for excuse, um, y squared the X t one plus two eggs and board. Why, This is their first time with the left hand side minus. We have three expert boy terms t x t war minus excuse. This is their second door on the left. Inside plus to one cute t x t y. I was, um we have six extra reward squared. That is zero. And this was two terms. Is be Derek off the factor with left inside. So now let's group over terms with the x t y. Or be left and senselessly bolster my left inside. We have or excuse Why spread minds three experience. Boy wants to work. You painless, uh, group all the terms we got the FBI or wife inside we have ex uhm cube minus six times X voice cried my street exit for a while and from the species that he ext you are is people to excuse my six x points for a minus two extra for a while you wanted by four Execute one spread minus three x spread boy plus two one.

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Calculus: Early Transcendentals

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Related Topics

Derivatives

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Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

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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