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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 $

$$x^{\prime}=\frac{d x}{d y}=\frac{-2 x^{4} y+x^{3}-6 x y^{2}}{4 x^{3} y^{2}-3 x^{2} y+2 y^{3}}$$

01:35

Frank L.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:30

Regard $ y $ as the indepe…

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Find the derivative of $y$…

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Find $ dy/dx $ by implicit…

01:08

00:50

00:28

02:28

00:51

03:38

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In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

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

Find the derivative of $y$ with respect to the given independent variable.

Find $ dy/dx $ by implicit differentiation.$ x^3 - xy^2 + y^3 = 1 $

Find $ dy/dx $ by implicit differentiation.$ e^{x/y} = x - y $

Find $ dy/dx $ by implicit differentiation.$ xe^y = x - y $